{
 "metadata": {
  "name": "cythongsl_examples"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "CythonGSL Demo\n",
      "==============\n",
      "\n",
      "CythonGSL provides a Cython interface for the GNU Scientific Library (GSL).\n",
      "\n",
      "Cython is the ideal tool to speed up numerical computations by converting typed Python code to C and generating Python wrappers so that these compiled functions can be called from Python. Scientific programming often requires use of various numerical routines (e.g. numerical integration, optimization). While SciPy provides many of those tools, there is an overhead associated with using these functions within your Cython code. CythonGSL allows you to shave off that last layer by providing Cython declarations for the GSL which allow you to use this high-quality library from within Cython without any Python overhead.\n",
      "\n",
      "For more info and code, see https://github.com/twiecki/CythonGSL"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext cythonmagic\n",
      "from matplotlib import pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%cython -lgsl -lgslcblas\n",
      "'''\n",
      "Gibbs sampler for function:\n",
      "\n",
      "f(x,y) = x x^2 \\exp(-xy^2 - y^2 + 2y - 4x)\n",
      "\n",
      "using conditional distributions:\n",
      "\n",
      "x|y \\sim Gamma(3, y^2 +4)\n",
      "y|x \\sim Normal(\\frac{1}{1+x}, \\frac{1}{2(1+x)})\n",
      "\n",
      "Original version written by Flavio Coelho.\n",
      "Tweaked by Chris Fonnesbeck.\n",
      "Ported to CythonGSL Thomas V. Wiecki.\n",
      "'''\n",
      "cimport cython\n",
      "from cython_gsl cimport *\n",
      "\n",
      "import numpy as np\n",
      "cimport numpy as np\n",
      "\n",
      "from libc.math cimport sqrt\n",
      "\n",
      "cdef gsl_rng *r = gsl_rng_alloc(gsl_rng_mt19937)\n",
      "\n",
      "@cython.boundscheck(False)\n",
      "@cython.wraparound(False)\n",
      "@cython.cdivision(True)\n",
      "def gibbs(int N=20000, int thin=500):\n",
      "    cdef: \n",
      "        double x = 0\n",
      "        double y = 0\n",
      "        Py_ssize_t i, j\n",
      "        np.ndarray[np.float64_t, ndim=2] samples = np.empty((N, 2), dtype=np.float64)\n",
      "\n",
      "    for i in range(N):\n",
      "        for j in range(thin):\n",
      "            x = gsl_ran_gamma(r, 3, 1.0 / (y * y + 4))\n",
      "            y = gsl_ran_gaussian(r, 1.0 / sqrt(x + 1))\n",
      "        samples[i, 0] = x\n",
      "        samples[i, 1] = y\n",
      "    return samples"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posterior = gibbs()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hexbin(posterior[:, 0], posterior[:, 1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.collections.PolyCollection at 0xb9c554c>"
       ]
      },
      {
       "output_type": "display_data",
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COPI8uemMnzrjrrNGu1tfnWxkrKFDiLbn7UvJ8sNoxz2NHVbxubxtrRFxHVXK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\nGmDmmXGcEeQ7BXar8l//xUXa9xSpLVQISinB0yntJwuKV/+a4F6G3ts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en69t0HHL7DQ4\naiMo6R9/eREx7vvuu4/3vve93HvvvQD89m//NhMTE/zmb/6mVi4CfMovyQyYHR1vTd5dQv5NCVNw\n2GWDu68IseBS+P53/CG7dpzHGsPD9Vu5v/YaJBaqwTJvHvhbojBBQstee45Bs0BEwqH0ae5Iv4hD\nMDMpxR8XZMFCyxK/EQoHIS0VmNi7jcdfcQQnhhYhn+PVpDYkcCnvnPpDbm58mdgUYMoiD/snY5hy\n8YfHsCWDxI6RP12i8liDdqnIiUOH+L/f+U5cYCg0Wvzcv/sNhmfncAh//sNv54HXvxJEmJnbxic+\n/80Y5zAk/G+vew8DlXkSIi6yg8tuBOsCGpR4jkOapR6LjQNMZDGBY7+c4rB7FhuHXDo9wh/983+G\nTQIcjvDNCWlVx9mtCCyog+08pCyBwwVgvrsJOy20wE4FcL5IGKXKAA5SUhuQJgF8WOA5nTbcXB3O\nLiDO6XkcGOsKK3PkzIzco3OCzkPZXJBdcBZlFF0CIdWUZItTHr0I0MlnyS/3i8AoqnHtUOA9ezk4\nRJ7rsYDmSQw8jDGK3tQOfVJMeLusFVmDpoGa37YMLPrjltGopCwsfALlPQtKNZz3n8vAt6ITo0En\n27rHi6eBE94uG4zsuNaPmebHhDmUAZO9IO1mvfR6O8V1r1xq59DT1riqoEunPr+tBcy8ACx6820v\njLMcoA/BbCwUh3thmHAJvS7wYzbJ+iCfFxOX/2qP2cZ2LyLGPTs7S29vb+d7X18fs7Oza2yM+ZOc\nI2nvRt/uO+RNIZTAIrj5ANpGX55Jyt7dp3Ootb0PEFwEQ8UFisWYwOt/jJpLHbudbrKjvx2cdUTL\nILEDA+FBkAjCtM3C2AAiCoA06CN1IakJSAk43D6FiOpjuxk6XO3WQKjBIgG4QCidbSMGiu0WF3bv\nwvp0Wf0LywxPz1GIdceTNx7urIlm57eRJJHK05YWqZY052JI0sHFjWg4vHEWF+p+Jkg79+Y2N0sg\nlqDQ5vLpMSQF21YvNy4HHQdQPATtQDF6oyHcJOB2eHpmCUwzxIZC4vHNOFFoCINqNFlfx3ITUq/I\nHYYQZBgKZFh1dqzsF0Ig6sLMM2tDx9lTTNqp197ZUzU49Jot+AlNUC8rY1GkiJS1j86wFq8VunXA\nRZa67LpvmAyH1u8Z11i3VX19mbfe1j46EGl4O8caDB467dPvi/6zI4dQsrEI/HGlMxj5C8luvnYP\nOcSRaZmzruQ/bD0pOD9mWQh63PVAXFuy/beqL6OxvXC7yD9gs7FodezW92Ojotv0Qamf22vGYKM6\nnr++zSfSq+nj1dptPWZnydgAV+NKf0UY9/j4OCsredDB0tIS4+Pj6xr73cAPAj+IyGF0drHwZzVY\nTnVFWUwzWQochmNnbyKxIbEL2V84jWAxWOaTARoUlXttA8619pNYxSNPmWtoUqRNRO1wibl9gySF\nAFsQmotFrNHJZde5SYqNNkGaMpAsMt6aJbIxoY05Xr5OF8wipLsNacVgQyFYtZiG83h3wOSd48SF\nEBfB9RdOMpgsErqEpeE+Jq/fThoZkijgpY89gXGqprJv9DRD5TlK0iBpBbTnejA2BQcjXMa4lLQZ\nEC0mJJcjxfgdtNMC1gnWCafT/bRsAZxj79HTjO6YISgmEDqk6UW2jcMNAhHqqZcSov6W5orEIcfD\nDK7FlVNIPG4YWIKyX3YmDvb6ExgBe8swYPQFYpogSUbmBinJlVeRsxCnSKOpkQ3OId36TmWUE64h\nlUiYsRmy5XpmGPuJJfNQfYhmEOB6E4iMLiuo061/LeLJ5SRokoL1zAxVwNJoRF0xODeMTvgBCqvk\nHpxIlpw2WwVkZR6doDOoIfOWU5TpkU1ObUSyCcYhkgW/CArHZMqIBpHuwJUsbN6iuuL5QzCLuNyo\nrPd489+764vW7LPWbtOqvwp2bXLJSEceFLR1HWuf/w0yHXMds2ATu63qWFs2H7PN9/nq2u1D5DVA\n9rd1+apg3MeOHaNQKPCOd7yDd7/73dx1112+wQK8B13WZvn+bkJnhTqUS/DKm+GYUbz0J1H21k7H\n2PgFBofmea55ACMphwZPUQqbhJIwNj3HhcW9PLF0C6/afj9377qHfrOEdcKcG2JadoDAWy/+FUM9\ncySDEUPT8+w+MUXPdAtZdSwXeuntX0WGHLN7hoiimMHGCnESsBr1sLy7jKRQfbxB/UCRZDRkwu3g\nHPt4Rq6l1Kpx++yjHB17nIqr8cX0TtqFkHqhTHu+QNuWWB2p0tdeZCSeJy4ZEhPSf7zJkdpTjDXn\neOrAYZ7ddoBps42VlSp/+4Fv4Uv/4+W0G0Vu/KNHuDQwxES8m1KhQRSkrDSqFJMW/6z8fm7sfZJq\ntMovHv9lLlR2Ui+WcF+O4GIBDumVsr14luHrLhEVY07+p6M0lqu6Wo400YE7baAJ1bvnKd+2SjCa\nMvcT24gfK+vcMw4cBd6ITuY/HMPlCBqimcHGyWWSJ9A5LAKGLsDUJbjcgMp1UBzO39/1+j/XhhPP\nQTsEeiBcBLkE8XkUK75ZLzIDjE5DfRJW5mHvATi0D67fCbM1+O8Porhz7C+ePn+A8ygUkjkW28h5\n0stotNAECmEc8H/ZUiNCB2ABfZD0oZP0NJpYM/OiPd7PPnIcOtNS2Ui3OntAWXRi3+//p749oygW\n3Y1x+/Fhxe+b8biL5NokG2HDJXRyW6/EV0IhmIyqWNzEbqP6UjbG2tfbWa7EyYW1Y9Y9FldbQv+X\n4fj/P8b9Dy733nsvH/rQhxgdHaVQKPDzP//zeeUiwO934Xx3eI/C4Hb0w3gvxgg2FBhVL8xFjlf9\n1n30bKshAjXK1KWCANuY4l/Jb4PV+j7Gm1lkkMgkWMmSnRmqLPOt/I1PNZYwzGUKLsakjupHagz/\nxjJiDHbY0vhvRsOvBYqfTQkugTMGVq2GhAcGV3Q0vl+wBYVUfin8eT5vXkVEwitrX+C9M/8BEFom\n4oN73k4rKOIQ7pr5DIdXTwPCUrnCye0HwAmBTbguPkHoUpIg5KHgNp4NriVpF1DJPbAuJI2E9/NO\nVlwfICxfGKA2009BYkrlGtfe8BQijraLOPGvbqI9XUYAe73AUQgCS7oA8rfqLNtEcHcLDHr8+xHg\nfvXMbQuY8gpmLX++BKSAasocVIfeKjSqXoTx20q+vhHgMBhnsTUH/1E0ilIUBkO8JkR6AeR+zV9p\nQxj4diQoABa3LNBWBTc7LHAHCBaXpnDfY0gcQxjgkkGQqh7LLgKPdS07M1bK2szo1g4Bb/J2KfA+\nYB7NXXkjcIvXrFgA/oaMauncbSh8YnFuEZi7QttCIY0ZFAunc9NdaQfOaRSTwkCrvj7jNbQzJkrq\nVwE9vu36YiC/l3Z4T9PhnGLreqwM/xUPv0ySZaN37hCwy9u1UOw/x4nz9G90tT0CtnXBKlMof329\nXQhsJ8vioxh/7O1US1ztVJc/H9t8bNbWt9GYlXw7apucg83r2IzN8bWyu7o+dtttPXF/xTzu17/+\n9bz+9a/fdHsQBKSpI/McOlhjXwlnNOUYBRAPd0riqO5Y7nQmdVHn8xizGOcoGPUwVl2VQFKsp6Zl\n3exlReVZve5vlHFbQygeS3TZjsWNgAvEp9mCYB7EglhNW5Z9TvtBjBB4EdkT5iWkot+uaZ/BeOnW\ntqkQS0T2CNnRmCH0fNtmwef1MiDiCNIUwRERc9mMgwhhsQP+gqQ0KbLqqh6KcCSrRXBC2xWolhaV\nBy4OY61mt8l2HfXAQ2rUC7aONPGD6GWrHSCTimrYloGGvhPI8jNmlbkmHfE5mx3A+IvMomH0iL6M\n7HcQKrClInUe73V5fTYFmAeXavi+6QFTULybAFKtz1qgz+PzEihtME71AdC2+kSx6LGod01UeqD1\n17zqQff7myLUY/lgD2sTNCjGH5eVrskdMn0T5wJUzF82uTlbVxx7Yw2Moq/PkWG0mtxhfdvVydE6\nMozbkQX5ZA+pbJvaRV3boPvhpSvfwNtlGLc/MaQbjJnWlz8sIPPMu/HaK+26sXsQKXWNWXLFhLZ2\nbLYas6xf8RZ2W9Xxldutb/v6B89WQlVXjtnmds9XXnStEr3Q9GRKlAUsgJtu6stDIV8NOnBt4dwf\nHSKpBdjEkFwKiZc1p+DT6bWcSG4gdiEtV2BAlv2k3dUhm5LUI6KFBKzeBAsMkTqdberfViTda0jC\ngLn5EU6s3OD52tC+wWAjsEaoby/TGCrhBGQVglmw1tAm4s70sxiXIlgeqdzKxeJOUgxhmlBKWuAc\ngUs5M7Aba4QUwbSF2BW0TW0hni/hUuWI77AX8TFApAQkEvnFeItb5VEi2oTEHN5+jKHCZYykBC1H\nxdbAOVIMfW9e0EnUuI6WNuII9sZEB9v6Q+qQB+mw3dwR6MC3PUBvN4aanUCd4KUrS5aM+A3WItNt\nSFIksJQLdcr9DeVjl1Ok3+O64pAqEOpsr5nSy3qQMEYqK95lt1BYJVtOy2wDWarrVW4c0puFlgsS\nJDmzJRyHcOjKtnsMWZX6HAqNTKKTTwuRvdlVQ+6ZWhRPyhMpiMx36nNuO5o8d81V7vuVK25pZpuo\n63vnCvWftS8iBdbqj2QvVsVj9W4DuwQR/1JoHU6sGXDyF3Yiha5tF8mxYfXqu+vvLnl7MwnZrL4+\nYIPrZI3d2rHQzOwZrl8EShvsr583w6RFljrtXTsWW+2z9bYXare+rMeut7LdbL+uX7vO/VXU8eJr\nlfwhlK6FaBcUdkHbeWqsUXz0rShEOIjSX08AXwbzAynhGxLa00VK/asMvX2axVY/xbTNOwd/j5Wo\nyiPuNtozJXobNfbsOMPe6Bw/+eR/YWRikXatxP943TezPFJhlEsYmzKaznGtfZqYiH/Z1YCUAAAg\nAElEQVS/9Ks8NnozDVfmD5Z+jNt4BFtytFtFlptDzI6MMBcOUThh2dO8wL7aeT563Tfx8PCtfJkb\nud4d56h9islgB7EU2JecZTYYZTnt4y3n/45D6TOYHTGnwoN8ztxJEkX0UOfuE3/P8MVFCrMJD7z8\nDp7bdw2toMglhjnPHoZYZJAF9nGGlIBl+rjMMA7D9ZxgyfXyQPyN7ChM4VqGPz71g8yZIWy/g4sR\nTEaQCtuqF7npzoeZLG9nNt3G3K9uJ3mooGO8H7iVXD/7JArJZlGUl4EnHay2oJmqLkh/AP+cTjAO\nH6/Bs02YbFC4Xhj+kYSR75nFOeHYGw/gzsTQjOGWIRgoq+e/0ISJS9Ce1rnjwLWwrQqDAo9OwtQc\nuFUIKhAOQjyrk3axAO1ZcNNQeTkU94NEEE9CPAGlgxAMQ/0xtUumfefGUQzZ6EXFad+5MjnWeh1w\nEMXVG8Cj5PhspnXS6/8Po1h5HU2PBhtzv/vJMe/JrjtizNcxjuLn51DsOvXHKJNzs/HtMeQpzWJ/\nwmIyposWR66l0vL2Wbg8/vcKa/neWR+77bYqfeSTbnfatPWlW7dlfRnw+0fou4J/CF/8atv7j6l0\na5gvoe8uXmSMe6uSTdzGCJYIBt6GCfRpawe1vRKC2wV8tz8lXsfepEABtu89w9j4NMY49sppfoWf\nAzSb+91/fx9TzV3g4Kev+d/56UO/RuhSZt0Iv1H6acQZrBGGRDFuwXV8DUtAb7zCT1z4XSCgSEs9\nPtGs8Q/0vpwPjH4n4oSKW+Xb5K8InaNtIg7FJym5FiEpi6aPC+EenAQErZTb/+oJcIaQhA++6q2c\n2nkNCRG75Bx3cT/Ggk2FTwWvwdqQNAi5X17FefbhMBziJO/k9/ztGvA7/Dht76EkCAEWh2F+bpiH\nHni1+k0S4EbRLDQWvmX3h/jGbZ8iMJbz9d38n8d+BqzBtQT7XkHmFJqyNwAv8cs1A+xUh50U7M/O\nIBOJjtnRCrxqAAlFJakvomH4icM+KciqwxQhLas3Ls7fWreL2olgPynIrAPnlSFXPc4nDuw0JtQV\nga0MQ1EZFK4JrIAxDussDAaYQCNx7eJfQXxCcedwP/R+j8cNY5h/DCM6eVm7HxhXqMydB/5U67MO\nuBNjCkCItZpIWO0yfFo9X2t3ey/PYO1lYMHbtYGprjyC4x1v0NqMF866+gzWjiJSQsRh7Qo5L7wA\nvKKTQcbaXNJAJWNnvF0CTHYdVxM0KGZeAy57XHx9PzIMfW2bcrusvuz+7cZkM6jD+fY5rswNubYO\n9WS7c0jKurHA56Fcb7f2uN12OhYbt++F2m3cxyvbt7Xd1mOm45TZbdVHPT+qDOmw9hdeXIz7+UoQ\noBi3AFKgk4/TU1tdhmUC1sOcRGD9yq2nUseEOirjzIITiqJvlSdru0g9B/lI7zEK0gaBBRkEEdrG\np3HCdnS7cWQS0QymiwRYIq/7q+iCkv6mou2qpS0QkIATnLFEtOlxdQoeZ0uI/MI2pdhqEqQpxioO\nONs/SuyXy32sIDjEOGJTJHYRLtQbYIEhEn8qhlhAEAwJlpCGK3f0WHCQ+s+1mmo8JNZToQJFKBDY\nVZmgEGifllsDGHHEYjrOkgOVcO3TsXCg7xnEn4MQmElw1nO3R1Xi1WmHAZ1UMAJNh8OQtoCKwyXe\nrgIY5znuwLLzQUVCdhEonq6sABuj28IIDVXHr+gd1hp90ojDutCvxmfAafotTL9e7C4AF4BLsU5v\nGk24kGGjK36CyHmJ2WQkoiHg3Te73mTqzSr31q6zS7rs8HY5T/pKvNs/FQnJOeMZZpx5zSr1kJ3w\nnCOuglI5Ju268FmlE+q2tOtY3cfNvrsN+pjZ5b+v5xqvtbNb2OX91W2uy85tWF/3tuz72rZf+ftX\nw65725V9vFq7/PetxwzAbWGXPaDtFe3fqHwNMO66/yBQv+hnaocsgo+jQRZBltFrbglNreXZT1MX\nd9NYreIcPLx6B59YeiMtV2DF9fKtRz9ET6lGZNp8evkulhjEAbuZ4AhPEaAa2AZH6BKMS9lrz7PD\nTiHO0pYCNVMhxdAyBc70/L/svXmwb9dV5/dZ+5zfeOfhDfdNepPmyZZkW7ZkLDAG22CohpCEph2o\nouIkFYpMRVWGKsqQhJQrlaI75XRjaDqdMIUA3aZANmDwLGxZsjU/DU96eoPedN+d7/3d33CGlT/W\n3r9z7nyfLMlyh13v1f39fmedPaxzzjprf/fa33WEpXiIDMeR5DUG81VEc6p5QpSnhier41R8O8s6\nBDlMvLbA6GuWbfzawB6+ect9dCsVNIYPXfwi4/kcqLLAGKsMkiMkVIglJSUiIeYAl/tLq89xJ89y\nB4nGLGXDSEfpZRWyLGJmcR8rrRFUoT7eJp700/NM4RJIliOS88jK+5nJ95IjjAzPMzo+Z8ZyWeHG\ncGFAngDns3yJBTeYvVkG7hxBnGUmlld6uEVzo6UFEiLJEqApHk8HFwmuht2V8wm80LGFxG4O4x0k\n74HmSHweF50n4KH9bekiSNIxL1MVF3dwLkAQKbTbBK4SqbwfcWN2WnIWSc75YwrxHj/IHHge52bt\nnpNRDMYQzNjNlfpQ73tIIj2KWPAM2xjR88fGcC5weUywNpHwHCEyQ2Qfzo2GYa3DNecICXOdG8K5\ngFG3MBw+hOfNeCxbEUlxrrzZpPC5ROb7GLLlyQyPdaCklQ39EKkhsnUMdTkH4nalnA9yqyKyvVzR\np7Vy62XXym3f3vr61klgWe4rfgxb93+tzrYf5xups53KWwCV/E9YTO4eYAKiBajFtgddBizX4Z0Y\nHcXn8VQQCr+UIh9RtBMx2FhhZHSWxYUJVpaHOTxxhtHheQ5NnON97uvclT/HcLTICkO0tcaUXGUf\nV3iZkywwwnI2zN3XnuH2lVO4iQRZFKKnHNWJDCbhjDvMa40DnN5/gjjuEZNxUQ7SocG7029wg15g\nLJ/jb+If4YqbYiBvcecTp3jgq48SpUAMX3rfAzx/4FZe3n+Uf7L4h9yWn6I7GPM5/TE+l3+Uhxpf\noRGv8ifyMwzQYu/KNI989f1cbh9k7AevcXT8HPu4wgWOsMQQbjXnSrKP890jxGREPaF1bZi4kdA4\ntECnZ/Hi+nd1aNmuyYZbZmT/AhMfvErySo2rf7ef6AdTonemzP3uPrJnqnBG4a4UGVX0L2K46mx3\n9ygW0qxYsoW/BW5Qw8PnpKDmOI9Burdhtux5hbgNUwkcacJIBV5ZhmtdWOrBLU2r8/kWdK4CL2G4\nbwX4KOCJqAZGoea3jncyaPl46Eih2oQ0gWQJC0fLMZw48Z0NG3AOYIslezGcMOSfdBiGbLtVLWY7\nwt5QZzHMNvB4BGbBcnFYJp0b/PdF6xuHsBfBF3wd+Hr2eGVmwGP+98D1rb6/g6zdpLOI4dPt0m/h\n0Xw9uO4ABW46QxH7LBR4t8Ni0980E/A2LFVMJ4OYrue2F/+ele85xv2v/F+Hao5l3lby/EFEDNdl\nDDhuz6+g6B+sElWBKhwYusBEfR7ncpaXhjn94u2ICpHL+Bd3/zzDlRUiSbnIfmbZQ45jlAXexWP+\ndnfc962niHtKnCfwmtqzb2RxyB2gLiITx9PvvJFW0+J1rzLJFQ76e1qZZq/fF+f4xd//1+yfmSFO\nEqSpMAIqQq9epXJXjzyqEJHxI/XP8mj8bto0aNZatuFHBFmF137xKBXNyfKIX/yV/4Pb7j1F5BLm\nGeMcN4A6elrhS/IQOQYP5IJlfxele67O3J/vt7BvhfwbgrGWKPlLgptT8p4gNyv6yz7zeAp6f9vk\nIsj+VQX+omKzocPAf2Poh6SQ/TW4ZY88BJsh9DcIOn/X5L9/BbeQWcvHB+H2EfPSRdHDgvNGIf/j\nZ3DXWn6aPQCMI+LARejofiOORMjnBcnU2qwqDPmYbO2is39KFBkGbXjyYB8CgSveg4lRfRDnAf88\nn8WoWMHwuX12DUTJ8z/EudTL+WlDyYgVuOQDOFdBNUL1NHCBYqaQ4Zzhklmm/azmRTSVYm+9A2tw\nU8v4LWumxSIJqpc2yJXhhzJ+ux7XXR8zjA85LGPSm8vtrr4AhZSx2/WljOWaLjaGZpqcXddCZ7qh\nvfV9ClnSdyO3O52t3fJ/fboty2kf0y/LmScv/TFen862N9xvCR+3xXH7jSUhXlUGKWJD6UeDqTNH\nPMB8tbhn6aQE0jT2C4tCnscMVZb6nNs96n1+64jMx1LnODKqvYTIa0y79FN3hedKNCPWjKRawfn6\nMvUkRWLQBiqk/ooNryxTSXzsrL8BBaWmXXtMPWZ+wR2ixYDJRa7fv6wToYmjl9n38ck5YudjU3H2\nwhHbip6rI4TGisd8EchXI1sEDCB1ClkII+sqecc+a9XOy515zVLRvm5lrhTv27RLlIdd3z2Pd8Na\nQM3fMf1w79W8wPLqQVA810oJ4271SsYxxBoLYXD9+PE8YOHWDxHsWnrQO8vCnV+mXs1LD6FSxCo7\nLD5Z+ufYwxUMZncdRll+iMNCkgLVEu5c8HkXeHLxNK7FRssec9mYyKYPcDD2m2GohQylY5vjuoUB\n0Q3921xud/WF3zZbYAvfA5a7vr71ZTs8udz+drrYrdzWY1xrtK9PtzvL7UYX16OzcnnTMW7riMNi\nXw9B1IS4BhOzOB+pJWZjzThFgn6mhsyDSM58OkaPGnnP4S5DdC4l1oSR+jx/vfRhlhkiISbH0aNO\nyDuZlLgYXrz1GKvNhi0+HhRkwpn9SMQW68QM1rG5szTTNi7NuHX6JW6cOUucJBy5cIl3P/k4tU4X\nFP7NRz/GuYNHWK00+NsbfogvHPkgaezoDFVZqjXpxFVaUZP/qvK/c6JyBkdGU7s0tG0vp0Eh/tlV\n4smE6kiHr59+kDmdQMi5gfOc5DTeXHFMzhC3U/IFR/svBkkeraOrgnsF3Iu5vVsGgIfA7cmRwYz6\nLyzT+JE21BU3kcFQanHQsaIXa7AiFs01leMsGTjyHPDn2Cy+DRy1GRAJyKvgXvNyXQxxSPAMBuPI\ngC2qyas57qIaJ/dV4EmBlQyWuzA1hPioCqnXcA3PVx1HkKegGeQ9iK/gnMXsSm8GutcgTxHNwB2m\noGmdxjnDf50bxMLV8BjzKQpa1Yr3aHJEZgiJMUVawAmKLOvBe4oQOYjqSYqY62e9fAZM4tyAb2vj\n/W6zS0FkAOea/rcEC8HLMOx6yf8miAz6/geuaWcPAhEwQIivLuO6RbtBbtDj7tYubN2/UEcZI95O\nbrOY5rUeZ/FbecFt/bnb4b+bYddvhdx2Y9xM7np0tltdbJTzXtoO5S2ASv4Iwwc95tZIYDCGyf2g\ng/Z8NTG4bxK7D6sQvatH7c4u9TuXyLIKiw/vgVmoNHrc+PPPMTk+zXE5wxRXqNNhmj2c5Rg1OtzH\nt7mfb1D1K/YdarzWPky6VOV9V77J+egIfz74MT5w6Wv8xMW/pHKkSz4Ovb2OTtwgX4kZvNJm0Q1z\noXKQPWdnab06xCff8UkuHZjinn2P0qyvMMckFzjERQ5yB8/yLh7jbp7ic/wYM0xyK6cYZYEZJnlG\n7+Cp5Xs489pNpLEwOjLDB0a/yr7qNDMyQYWEO3iW45xhnHm+xbu4yj5enr+RJ3/vPq598wA6o9Tf\nvUr9nlXafzFA9/Em/LTAERi5ZYEHb/oi+ycu8e30Hs5+6wQLXx6HuzKYUPhiDRoCd4ph1C9jMd2v\nUGSBSnuwrwVHHNw1AM/ERletGCx4xF+r/Rj23QIeS+HFabi6AuyFygjUxAx7CtSXgGXoTBtn98AR\nqy+5DN2XId5ri4mrT0Oy6G+EEO8b+G3KpWP/3QqMHbTUaXMzsPgqhp87DL9s+DqGMKN51v8WY2+t\nCkXcrF9ApwncbuNgBEugEIx9RsFrnVNwiVR8e7mNs8/JMbhOrlwctotxH/bCWcXizHPfvwkKzo8Q\n10up/bDZZYyNJE3qj13j+nHxrUrVjyel4Ez5h/LmlAi7zr/yvYVKzHtJcG7B8LGuoB1Fu2NI3fIg\nYvQKhnEL5PeBugrtUxVWpwdxQwp7hdqtbcYeuMqCG2OZET7GX9LAMp88yrt5hrtJiZlnnPfx9+Ch\ng8/ykyT1Blld+L/3/BznOUrXVTkzfpx/lP05UVeIrghXD02Q1ivQVM7sOcoVLBHCk4ffwS+N/Tao\nQ68Id04+QV1TDshl5vyWma/yAR7jfsaYJSY3bJ1vsZdZ9jHNpZkjnDl7K2ke04jb/Kcnf5tYFCEn\nIqNHnbMcZ5kRDnOeCeYZ7LX5nf/ll1GNYR+M/bfXqN/kPeljSvf3m8giRM/n/OrP/ffEFeP6fvqf\n38vyNyahGyFPxhb6J6bf/IDtMtc7QJ8GmbPHULIeujCNLIKcgfzbA7iaGhQzhoUOdv3fHydE55H/\nwVO42R45OTRqMGA766Rh0JdzxiqV1w/4eGyg+wK0HgfNkOQsmuc451DJUT2Jc8MemlCC4Q64pXN1\nVOvoiffhhofIJTb3fukJ0AznIvJ8COd6qPZQfQWjbM0JlKwFXrtQwqQnEBlAddpj4lOIjCAyTJ5f\nwLkc1RaqLcJWcaN03e8xc8jzFZzLyfNVim34hWdl7Qp5vh/nKuT5CvZSWMJmBDGqZSz8Cs5lfipt\nfB/BSzfsOvS90E+Rt1FLOisw5HIMcvGMFjOOIFf0uYHqntK6wDJRZHWsH9vaMeoW9W0utx5+2Ulu\nY9/xOtv9GDeT243O1mPc243ROcO4d6+zcJ9tb1ffAsNtN1fAcfr4k0TFolcfy/RTB2c4tg+s7mOe\nUskRsZRbKY6KJuAx6S51Mo/8VOnZoqffIptqhdRWzOiKUb8CVOiRS4SohfrlkS2liWDpzBAQWBXL\nFZl4ddXiYgtw6mNvQUh8qrPUT+drIVuMQCeto7lNgwNNbSD/ydUbKY+5Kw6RHM2ULIv6+GrUzJBa\njnpMWHwcfJZBpZLg/Iphu9UkT/zd5fF8zcX0HXtjLBRZo8ASGnicWBMA52OrAac+9l0I6RL78HQ7\nIw80ry4kHvDXUTwGj13HPID1miDkdr3zsPZRYNcFX0qxgBQOF2IxeaDzzJK+7sImkwLnzAgcJmtj\nikN94Qkp992wbcPCDcfbDLsu8jWG+tbKBY8ptFUsWrpS/8I2+6K+4piW9OLW9X0tTl6uL+ScLHR2\n/Xhy0WdZ166SbZIKc+MYt6rvjZHb2Pfit91j5hsx7t3obCeMu2yUbX2v+LtZPTuNcbMSffKTn/zk\nriRfR/m1X/s1VH8Su+kWgYv09+MnFywVZX0MGRbLLt7EeDD2gzRziyo4khCNKHGWMTq2wODEIr1u\njfRajRefuo099RkaAy2q0mWVISJS7uAU7+A71NIezW6XuxefYdGNsRgPMyWXqZAxzyidap1uJWbP\n4hxnkuP8zpVPIHXhhtpZ9i7OUuumLNcHOBxf5GTtJc52jzNQWeFo4wzjjQU61MiIWMViwQ9whRt4\nleVsiNWsybdX76GapTR1ldMrN3N65RZSKmR5len2XsYa83SlytPtO1jOR6m6Dqfat3Oxd5AxN88l\nDnN+/AD5UoWh2hJ3HXiC8f3zTKd7SKVGt1OHyw7pCGefPc7kkRl0RJm9ZZRrvSmiuYwTD5zm4D1n\nWZgfJz6S0rhnGTJHNhPBnBgW3cFzYgtIhjRiGK2YN9HLYbGF5Ak0q0gLaIkhELPAlWHcTIJqBpUh\n+5+LEXl1ANcCnYP2Y4jLwI1DZBukSOZwrkGRvbuGZXwJiWFHCOm9QkSBYdI1WGni4iYa9aCdwUoL\ntIXICMaOlxK4n8VnxCgwxSrGuXGQEH1h5wxiHCaBL7qO5YIcweK6U4z7pIpxbGcEHD2051xB1rQR\n33QYtFLBuZClvUvY+m27JH18KZlvI9CtBq6PGOe6GKtg3etsxMOSbV+XkbAVOnO+zkGci1FdS826\nGQ5b/Jb4F1/s9dLrOxw7n7u730I/t5ILxTmHbUgaJFDEbodxrz13rcHdSW4n3HunMW43nt399mW2\nM81vusdtU8EZws4wS8FUh7yKLo1BxbxGrgCroEeB20Ab5mFXJrqcPP4idww9x4KOcnb6BLPfmCJZ\nqrIsYzy8X9i75zKjOg+dlGZnhT21q5xvHOGx9H4menP8k8U/4j+7+C+ZlgmemLqLD439LUfyc3zH\n3cN3pu7h081PML84wTOv3cnQ8hK3DT7LRG+OK7KPv9MPcpOc5o49T/ETe/6EFQa5I32Ge2efYqjT\n4uGhH+WZyu1kbUdc7THcWMblGZ2szmo6xnP5bSRJlfPdG/jYyGf5+Pi/5on2vfxO6xP8WfencZKy\nsjRA74UGXIqQYym1W1b5RuW9pGlMa2qAkfe1mMjnGJ+aZf7lcaZPHzEqWgWugrbheW7j5VePEQ91\nqUUdGEsYjlcYGZ9l4O4W9YE26WBEZahH+tkafKUKGYSNeaoC9w/BTw/ZVvPPpeRPLMC8xRXrcgNm\nsSQNCRae3AMWh8iHbg2VQGcVVlZRakAF2ueBaXDnUdeE+ARIxS80dr1HuYhN8WOgh+pZDIc+jnnC\nlzB60bo3IjXo7Cc/s4RhyC2Mc+Q+bBv6DLbxK8V2Yd4GHEX1DBZvfROWEKGHJVpIgQlUb8AYLM95\nuUn/APawNGUdoEpgDbRjIYmwLSzm+SiGCS+j2i7JQX9bMIpRx5aYuxjA0oktU3B5R6iO2HhZ8Xpa\nXDObsHOHUA3c1AkhTjnPe8CSN3YxtlM04NUr/XbWe7kbf1v249lJrvw59i/kiu9DZ8tzN2Po2wwq\nMLmYkCx4c7nIX9O6H+Pqhja2PreQ26yfm527O128vt+2K28BVDLjp6gO1SkKzoMfwLkp8llB5n2H\nFeQ06AdAEkGJeOCev+fo4FmcZCxOT/DKo7eSaYQMwa0fe5IoyllxQ5xavJWFzhgZES9zM8eaZ6AG\nUU35ped+i6G0xTDLHBw5TzoU4SRjMp8jj2LyEYcOO37hyO8Qq7LsBnm48RG+KfeTSIVXOEmGC/vP\n+NWLn+JAcpWIlC9kP8yp2h30qDKd7WNlYBDnlNF4kY/Xfo8xFokk5aPNv+Td2beoSo87h57id2s/\nTxPbUr78tXHclSp5JjQm2wyPLCGxUnEpi0/sY14HmdW9nL5yM5FT82hfAf06kIJziv4PbfIIukmN\nzqeGkEdjlnvCtWv70UuCiuAEWv/vsGeJFZjD0pwBchvor2Jb3xX016dxy7mfxA8brtoSQyT22p0j\nNdD5Er7aXkLayx5u6nrPxQiadPi9uEpksFDnIqyex6b1HVQf956G5VZ0rubjZ6/2p+frcUHY4/Hk\nOiK1PnwgUvH1hdyR9+PcOHkeITKE6qy/L427JMAKcC8iN2DUrSOozpXa/SzOpX4a2ylh1zVU9/p2\nQXWgdH+3+zBP0ecEkRTVVkluxLcnHuNeLGGoe3GuSkHruur7HnTRAlqoOpyre13UCWGFhsEvGOym\nKTCM8X7XsbyYrXX1FYYjXNP13uN6ua1/m/JtgeX13Prc7TDutXKK8YgXiSPK8pvpTGR1TX3r8en1\ncdrfjS42k7tePa6PQd+qvEUYdxFcX/Y++jwM5TePDwv0Z+Nc3t8OnufOyxqgWY6cUZzHtUGNFQQR\n/DYJw1MFfIKooJnwtgCR3GoIcdzOea5nyDQqN0vkKV0BUo37cv0xhCmgX3gEiFyOBI4HzX0frU7J\nwxWU8K/onwadmXwfMy57KVBEkQGklnTZ9O3XEiLQ3Ne3CUbZh3gFe52ETTDrS6mdDdd0S89EDD/3\nevLI8BrxtVwVGyvceP8E/m1bHwjGdKPHEnJWbtYvXSNXOur/S//z2nrDl9KVCtdoB4+pwL031rG2\nrrX1BUhnK06P9THoZV1s7T3a+LbzKHf6bbuysy7C3+0FN5MrG721bZV1tp1uN293Z519979tV3Yr\n/xZg3D+FxcZa+JPxIwxhYSTDFqK2B4tsqoAcwXY07ldkPOfyyF6yYUc1Tbi8cohr3b3k4pCRnMVo\nkGojwUU5WhUyiRjRRW6tPc/J+GVy5xhhiUvj+9ibzzDGHPkQaAOuySRn3Alec4fIJSIl5hJTCBCT\nEpOSEXF29RiXZ49wfvoYBxoXORBfJBsQYjKmdS+PDL+HF+o3M6Atbqqe5pbKC8QuY5hlJpihQZcF\nRviaPMhLchONCx2+8vgP89jD76G3v0p9pMP4sWkiMlqLQyTVKlk1ZnhknrF4kYN7z9FL6mRVx8DN\nC8TDPXpLddgvFj65CLLHk/zXFdpiiQdWHXTFIs7GgdkEeaULL6zYi2Ighj1iM8oqtlt8BFhNkGe6\ncDrBaKg9pkwF9omlMrsTmMX4TbrY+nAK9KqQOajnyGQTJgegnRiXSq/jsdYK9AYgrQLTHjsOZZAi\nxViOhQUOYPkhjS7VMN/MOtDflXgeg0wqiBgEUWDDcwQc2razz2FrLoYHF3jtZT8IAZ4GXgSaiCxT\n8F+X03sNYGGDk76e4DGG9F4dNqb5ijFu8BGvi8QU6N0LkQ7mWfuYWKoUuSVDXsrOJphr0KFQhDcW\n9YW+FaGVQ77fowSmQ+v7+nrXlu3w541ybT9G9WNMKEInB1irs9ff7ma6KNYtVgnX4Pr6/naQ+55j\n3Hnxv7IXmreDDMDqKiSPQ/4aREfhx2+Hj1Tt3noMOAVag/ZAkyem38V3zr4PmVAO3H2BG254mR41\nXu0eYYFR253oYGCwzfDgAg3aHOAyx33W5IsDB/gvb/pf6WmFn87+hKa0eTj6KEO0qEubOSZw5Bzj\nFcZYBJSlxSanPzPEI781jr5zgPw/30vSfBf7alc4NniGsT3ztGgyl4+gbSHTiFQrZN7PVpQVBrnG\nPs5yhFba5G+f/VE++TefQucdWs+pLa1QnW8wWllADzvPLy+054a41jpEMjDPOw59i/vvfxRF+Hb7\nHp4/fZc9Cw7L+3gbdm8uRuhLkdGudoEHgA9hMObfA38ltqi4MgOVV6HWgdvvgIrMnSUAACAASURB\nVB87Brc6u8e/DHzWy9WqcLxh/CHTYseHgJrCbBueX0FXBeJhSGvWZuzgxiH7nwDnXgAeMcue3w6t\nIayDe31lB4B5GBmC/beCVOHiBVhZ9E5twL/Vf55C9V3++/P+WIJhmWGhJHyfxQz2OBZul1FgymHu\nVS6rGLtZiJkewLDdiHIigYL3ZNLLtCn4Phr+e/llVC6BMjaMB/95mSI3ZuifYka85dtvsnVZbxVW\n2JwvO8Ni2rvYGz3aRGanUqUgZV/EQizDMcPbi3bWx7Br6f/uy/V5rSkFb8x3W9ebU9bPFl5PedMN\nt8VvK0oKw/d5ilIB/TrCFbSryC1L6H8QQc1P40/jp7cOnnT27CHsqV7h9hNPEsWWHf1Sbcqm3+Ft\nBSwxyiwtKiXv6HN8lIQq6oTfl48zwRwqQpsBiikx3M4pmnQA5YufupOH/7d7yXo9pLqAO7mPGTfJ\nTDLJSXeGMV1gXOapt3ssrYxYdIkO2A5F325CRIXMeLuf3cvFrx4jr0TIYcX9ow6Ji0nSmJXz49Az\nrCKcu9odJE1i3nHiSSL/kF97/CCrM8bFKqmHZGJQn4VLAy2up2hVQF4E/TyQxGglguxRyDN7Qd4H\ncofYeaeBPwZ6MUoEN9f93SEw5OtbAB5LYH6uePa6MX16wJtAbrR+aXcGXv5T6KfkOta/HuYVK6pN\ntDIIJ6aMJAUgPdM3WyJLHpNWfz/cRYHVXPaYMITdhRa+VwEulqbBBxAZ8xhyrY//hvyJxQM02zdC\nFrs8QTHtDgmCAcaweO+Q3OAqBdyw1mBvfEBDFMr6TUX4/q+XKycBXuzXt/Gh3+PxbDzGv7a+srxh\n+quInPXHNoMxN8dh7e/+EvQkJfn1OltrtK2eFJGNi5ybtbvbspPs1jrbboxb6yIceyP6vlm7uy1v\n+pb3MgevYZH+jSuuiJpX7fdEvL3u0zFmQgCNNSsw8RjDvis+Brv8Js99KrJQHDlRiJkOu3xY66cI\n+M3y1oar5hCZRORjsQ31tu30gXckJu3j3X1s3XdFVXzsNn5K7tsNdC1BTmRNX/p9V0sYoR7bj1xK\n8chovwLJ7K/L/R1VdujCq1nUbKO4AvvrZVBaFAr81+ItZz+LZ2ktwV9GRMrX1LcRMmFZM/16xVfe\nv/G9rvrtYgZFfMXlByRUWEyrw3V2RbsUN34RYrZJp0oLA2E6XWxjLg2yVIrtyeHYWpy16J+skwt1\nrp0GF5/LRm/j383kNpPfcA22aHf9uYX3X9bZhqbWtWs3xlq5sl50TT2b9X2zcWxGvfpG6Wz9fbFW\nbus+ba6zze6zrevYqr7Nym51FsqbjnHDQ0DVgOXeJRgchfFBuOkIjDTgSA4fuAGOjxo+2gEOggZ4\nKjwn47CqAywsj/NA4+s8uPAI/8XZT9OKmpwfOMKQLFPFcloqyjJD7OcKg7S4m6eIsAXFW3iRPVyj\nQ50mLQZoAUKFhFkm6VJlmSEuv/dGWjePM7Iyxzt/6gz33/c07foA9bjN5cp+ssjRoc6ZynEW41EW\nuiNkWmGpO4ysCp2ZAV5+9mZai4MAXJ09wHJnCF506JOC/j8xcggYFbQbFS+lUJYgm454/sk7kJqy\nKKOcT25gIR2lOtyheXyBxtQyvUci9Atd+L1FNHGQVuDLYrDvSWxGfxx4tocutSEZR9X4LXjmIEwP\nwaDAk5gD2VmBfA7mzqIVgeaAbWGPMTRBIqjUIFHIDftWn8yCeWzGH1+GSxdgsY0xVRkPtromDA3D\ngf0wOgyrCnETehXI29BagNYy2mv7yi76v3V/I5zHDMUycAbVAGvM+d+a2JRjHxYWqBSGu4ulCruE\nQRqrWJhfiFLo4Pfo++NVfzzIBaMf5KRfR0EVOopq3fcjpENboUh/Jl52zOtMvG4CxLKxbO+JhW37\nNe8Fdylw3bDtfsT3d20G9+tvK5RVb/BzCl1AyONpHrdh67rp6vbrbfftKbf7Bdjrldse437TuUpE\nPomqs6ncyDuQG96L1odAUuTSErrcRX6ogf4nwzAQGQRwBgsLtDUW3AjkQ1j42csw+fQ1Toyc4Zd+\n4Z8y+9AYFwf2c0mmqJKyh2nmmEBRbucUVRKqdBlgFUfKOY7yd3yIlzjJJHPcw2NMMoviaFOj4g38\naxziKvto0mJIW8y0x/j26rtIibhx8CX21mbJBDJiprjK3vwqV7oH+Pw3P8z8V/dBVxi6e5GbHnyB\nkYlZLl86xJVsispoh/xUhfn/a4LseLVPN+FOQ34e5GbQ48A1c6j16Vnkq6+h3QQ+cZDo58ZgOKGR\nd9F/GbH6G0PQzdA9HeT2JtqMYU5wV3wY0p2gtwIvZMhShj51GVmY8Q/VpIW56TxSH0EbxwBBtIsy\nh0yNoc1BSAS5DHoNpGboPb0WRhE4goWggS04XUT1AhaGdQ36C4gTSDRsC6cT+4BDcC3CVSGXaeie\nJWzVtDC/BFswfBXzKKuojlGO4d0YauU8HLLHwyjGH2LwQQ0LTe1h8EmG6jks5DDBNraMkOcDvr4l\nilRm5TZCuGATC2Wc8/d6jGoD27CSAXuxMLwrvk/9Nx+WZizxL42mr3tlk6n2MM4dI8+HsZfYWSAv\nhc85wkYl5wZ8TPwKIoseGqpi8eorBMP93Yf5rf3tja5vs9+s1BAZ9XpcxmC0zeGJzULqttveXi5v\nhS52J/dJtjPNbwHGLWRZjkoOJz5kGHcGvDiPrvQMKmjlSMMZ97MAT5UmpGOQ+yADPQ18A2bSPcws\n7OGDP3qSqJJTp9tfiAS4gbOMstif6o8x1+eFfpx38Ry3Yqwewh5mfcheRqUUBVCjS40uGTEX0oN8\nc/n+PjwyVFkBQ4I5yHkOchlxynhrlqWH99jMAXjHQ48xuHcZBAaOLdFgCBWBe5XsiYo5LV3gm5D7\ntSS9DDJgetBOBr/3Qj8sz73DoYMpqKP1bwfhf66hHQFiuL9qdQPMQO6dUX0R/3xH6GgEi2X891Kx\n4SBNsKSVDqUCRwbQMIW9BDqDXauObeoorlCFgnv6EqqXsFDPql20/iJbDc38IvVVDEtRyDsdjPGq\nuElti38NEG/8Qn7HgvHR5Hzf+zd87r29qvdAI8y7FS835eUCxv1a6aEfI8+bXm6VsCi60RMaRXXQ\n/xYRIALrX68kd6F0biCxCiUpya1s45XdSZ7XKWAcDwX2DVBY+K95moCoJKdeF2vx9I0629wrLP+2\nndx2G1beqN+sTNKf2W0rt9YYh75vtpV8M7k3ShdvhM62K286xp0FgiMRyDOc+LhsVyRCZdlihkUx\nzukYorDmmFFgwlUweFyJaxnd1RpGbi/kmZCldmETrXqlOfNaEcTjz3VW/WKfkmIVqjryzBa6sszy\nBro8N44UhYoPLYs8ep7knp9EsUgStVjhKFYQ2yjgIiVZraBqBkpStYXXHJwIAXN2goVBhnuyh5FC\nqT8WOVzseUlmU6NVBSNxCrqtAJkQBZw40r5uJUshN51HKMQRLiouex+DI7d+ilqC3xyfkllLwQcB\nSzWc0zkzHM4FOMIMv9Xr1wqceAwzK+GBKf0Udr6frr/koX3OFdt9J8X9s0ZuI14rEvBSq6PAxcMT\nmvuHKlCoRgRCfws5DPLSH2sU1jmiIJdvKhdw2qK+ohR9lzVy60sZN7XjgX9GKUeAlLFh00VW0pnr\nG46CjrTo03q8tixXjHF7uc3qK//dqLPN5bbX2Xpd5GvGuLkuNup2s7WP8jjWj7Es98bobOMYd6uz\n7cpbQOv6W/7bCMRHYPIAVCowfRW6DqpHoN6AW+rwS2LP/hUMjrzqP48A78cs+QLszS8zduMMN/zE\nKwx2W3TODPDEN+5jcHiFW//xk7ycnGQpHeKXRz7N8fgMYzLHNfZwhuM8zy2c4ThXmKJKwiQzjE0v\nsjAzznOv3cmRybMcHLvIk+feSTtqcO97v0EU56ymDV5tHyOVCpONa9Tp0O7WudQ5wCAr3LnyPBeu\nHeW5l+9AOjnV8S6D711grDpP5fGMS18+zFIyTPNnVujN1mi/MGheZ4BEXwX+DZZysAb8KBYJ9lIP\nrkwb5er+ffADNeREhv5lBF+MYK8Yjn0EaPdgrguvrkInguo89C5AfRlu+kFIhuBKCgsXobtIn6K0\nCtTGjXY16ULSg2QVxgahOQjXxG/aCzSrbSzcbgEDxm/CgrsF81RPYcYm8d/99V/jMQ9jAfzLGAVp\nqHvZK6CBefYL2FQ/bNUu+xo51rGW/7wHu4EiX0eGYdpNTEnT2BTngD8vxG6H0vCygZR8qxLk2hSU\nsFuVpv8fY1h8bwf5cnFY2N6o7+vCFnLi2wjbvLtbyH0/F8Hu1yo2xuvR4/dj2R4qedMNt3P/pzHZ\nSQXVE9iNKDCQ4o5MkjeHkUzgMOhx8x71CLauIyCXM9wdPfI7cuqzKT/gvso7b3mc3EU88rUH+M7v\nv5f2TAMZEWQUcqe4wxn6gFIlYzRe4EeO/iXXxiaZYYJhlpniMlW6dGjQpcZAukKaVHnkyR/gwuVj\n5qFHICOgzYzR5gJ3nXyMRn0VxXFx4RCvXriF1uoAbihBxhKbxK4CKxGyJ0ViZXBomWalS67Q/eIg\nS/90nGwuQoYV/YUE90AKsaJ/X0H+qEJ+XsyjPgx6EiTBQvDGsOf+ArhLFmHnWqAp6Jh56zoGxLnZ\nr9NLuFdWyLMcI/eqme4jBwOCVL3n2b6CdL9Dns0h1X2ouxM6wTudRuQMqm1EbkLkGHne85jvIv3E\nACNV5NCtaG0EmcmQS4vk6Sq25f1Fipx+k4gMr/FsDOdTjBvknNXHGM4N9jHAIEc/3jnANHWM8rTb\n91Cs7oqHaUKy3yrOjZHnNZxrozqLUbwadALHMGPwKs6d91ugI+AEqgewl89ziCyU+r5xq3Rxz7OJ\nXA3VSejnjmwTcG+RFUQWKFJpDRGSQlhSYduyXaYt3Q7XXauzjaUsV+hs6/rK6cJ2and3unij5HZu\n93uls7LcTvVt1fedDPfrhkpUlc985jPs27ePU6dObSkXppO2YHOAvkd0+BD5wAiI0H9+xIwRB+gT\nn8lHEvSuHInghkOvcM+tj1OJUmrS5Rv/7CHa15qglqIrB8iFvBujSUw3r3O1t59nhm/nGntQHMMs\nUqeDQ2myypjOU40Tmo0WV2cO9MPUdADyuuGYqUbUqx2/bSPn5Vdvo7U6CAi5gxByziCwL0MjIVdH\ntZKisb2M0hlHPu8MqxfFPZRAQ80J/bOI/DUBB3pM4Wa1+OwGMKWmixhY9nzWzhZrGfPXIsWYFCMH\nFYcsJj582nnjdNJ0nomReuFAHJq9RJ7NADna60Kn7H0+hzHQZR4j7PrrHlLgiHXq2H1oYxScoN0V\n8tSTUmlCsQkmAxprcLwC52sDZzADGfDaQq64d3MswsTjTayW+lS+LxMKDxwMuzacuEhFFs65jeAN\ni6z0cVBbBD1IIGaCxXV9L9extmwuF6AO5+sc8i8Xh2pWkosx7zoE5Hf79eX55thoXzub6mx7ufV9\n3kxuMwKoUMrGLhizcvnudLaT3NZ9/17rbLu6dquzncrrNtxPPfUU999/P83mdju6IMty/0bLgRTn\nUsNGuwmSp4ahdv0bUj2unYDLwOWgbemHBbZSS/GUZxFpp0pzpIUL8ck++kvAr8cIzteZ9Kpoalhz\nl6rFa6uQZsa5nWcxeRLTrK/gcu1j61YLJGnNlnvyCNRRr7aNe0QVelLg8N5euA64LqSJg1UxIqhR\nM4ACuLagPS+noPsUqXs8uZOjuSJ5jqTmQbs8J4pzaIDUPcbqaVucs2QMQc6hFlkSiW8sN8w+wtKU\nqa1BOge4QYgie7k6H3UQ4bHEKpYEVyiIu9VrJGDcQLeL08z6XjFidcOAIy8nOJ+puIwhQvB0Ahbu\nPB6YegzaZMqeGEhJbi0maXJSwpPL9QU5hyUgCPUlOJdh5PX1fp1hkdG5fI0utkpdtR5fLWJxC1x8\njc76GLz1qahvvVy0hc42trtRF9+dXHmMwXtdjxOvNzImt1YXu9PZxjF+N3JvJ52t18X16myr8l1D\nJceOHePhhx/mtttu21i5CPBDmFuZY0DsR7CtkJdhcAKmfsS2WFeA9+QQixnDI5gH+7LCVI78+ym6\nGDOULHNX70mWzw3z3CN3kCUViNQiOarAzZiHOuibq4IkORM3XmH0phk6cYMBWgxcbHNl6RBzq+Oc\nbL9EcqnCK0/eSLqnZgyhQ6VuC1QqXY4ee5HaSJt5N87S6TGW/3ocnnYQ58h4ij7m4HEHP5MaHPdw\nTO0dHSrv69D5twOkL9agrkX6wU91cR/LLJrm6wr/9YKl4YpTuOWYOZgXOsQfr9P4SaH+4ArZCxXm\nfmO/8YzEwJeX4VoPljpwYhimBuxlsdSD+Q6M1qFaNds7BEyJtd8G9ip0ZuCFczB6CGqTcPoCtAPN\n6jL2RhzyCq37751CMeJgZAoaR2A+gk4P4yyYxWCSBqaMYa/Qpq8P4IVSO9coIiCaGFa2/g7OsR15\nZW4OT+SO83VVfD9XvZIHCduzC77qUBy2/b6BhduVj9WAE15m2Y/Foom2L00Maz+I4effKrUVduq2\nKEhiWqzF2dfLfVeP5z+U75ty1v8P5cuvH+P+8Ic/zNWrVzf8/uu//ut87GMfA3Y23M79WikUZwR7\ngB1yZAoeeg86NoJcyZHPz5Mvd6Dq4JfH4aN1qID7FvB1jwkNABdBn8dg8l9ZZPAXF5Bmzuqjw6yc\nHicfFiM/+uegT2DP8X8H8kFFI6gNdiB3dFvGRy2PC3qW4vnwb0zZh2HmLQyy6YBeUcQptR9bIbsZ\nsjxCvhqh/2ON/KpYHQ8B9/p6OiDvBN0D7nyOjHTRO3N0RtDfqEHPXjYylsHjgp5zSLaELM+SZyGz\nzjDEAxAL9Qe6ZJcikhcqyGQXqf89+WsXsLQ0d4EYduKGhiAdJl8VS0gRz6MrbXspHhiHbsMS+jZ7\nyOI8+UICjQpSnUCXIiz85SUC54NIF5Fp8ryDwQpVD3EIBe+Iec8iz5PnF7zcXmwLumBJCRJUU5yz\n9GZ5HnhIAje1+nqCZ9NEZJIiIw4Unn8PkcjjxCF1WDi+iBnbHJE6Bvckm2CZQ/6edIgsIbLYx1ch\neEcOW9gMHvlyH5Mu97V01/vfRxDJyPPlLeTo/15klN8otxleu1nZDP/dKFMHxr3OOojMkG8iuN67\nLHSxWd93xnV3GuMbLffG6qwY1/p2t5MLnzfv+26w8O0x7m3juP/qr/5qu8O7KsWURbCHxH7Q974T\nxkft83wHVjv2zKU5/FStb0D1PP04Zj0Hcpo+jDH0y3P9MLokqpOP+LpfAXkKg1gS4EEsJlmhu1zv\n94E5q7+0x5z+9vqOoi0vtww6DaiFFPYO+NAsB/nzDg3vtnHg3RRavR/DqYH87gw3luP3X0Du530J\n6N9ElnldQJMI8rDJxHuUqUAKnS/V/aYX0GsXwV30Vz0Bxvrj0OUQxwy62kXE67ansFzvD58rS+Rd\nH7vedtAJgH1MEQ0CqgsEInxIMZ4Or68S+ZHqC6he6Pe9iLtVoCAjykOQua9vvSdbYJkRGylZhfAi\n2Dz2NRjucKxT+ryuKiPB8aW7Bl8t7tscM9qyQW7zEupY2BETDb9vRdVa/r4TR3NZF1u35Sk4wV/D\nrcdRrm89Dlsu2+G1a+V2njnspIvdyr2xOlv/+a3T2XblDYnj3u7NkGXaj60N8abOAVdnIE2NG3vU\nYqidz2fI5Qxp57ieont8Rx3QtMOuClKD9GwFeoKkQjRqILdTYNyMvauCqwHnQVIfn2w9Nl6PioJC\nLBmNWofIZdSqHSqVFMksPjlyuUExBMwKdDoy3DoDjuY2M6jSXzfrY5QB806Bthlf1wNxCjVTvlOM\n2hbDl6nGqICLwxU1TNu5wCuS2xoBg2iuOBdhb68O4rEyW6ALnBKR9z4UkQSyHkIPJynqYor42KyP\n69p6RMPPmMCm9OGz+rpD/V1EQh1NLycUeG3AuPHHHMH42ufIf47WYIUBny7GUdwHa+uzPgXs2uqO\nEHGb1FdgilYSr1vtv2TWyoUHqyxXKe7HUn3l2PLN2g2fdy+39bHrlwvfjULWrlVMiH0PxfpUGKD1\nutitXKhzezlZJ/f20tnGtngTdbFRbqfyujHuhYUFPv3pT/Obv/mbfPzjH+dnf/Znec973rO2chHg\nk1Da9RV4KwCYHIef+jA0KuYN/uE0LKZm0X54GG4dgm+bV8o7KYJSTmHQ5QmlelOH+GBK+1IT7UXw\nCuZwLWDMnw0sqOIdCZUHuqSDYp7zn9XhOYFrwoM//CXuvfdbvPfer/Odc/fxpTMf4sb7XyDH8ae/\n949JO1X60WgAQwr7cjicw1IEMw6+AdwIHAMWvJGdiM2Z/ApGrZor/HwKsw5edTCjBgXPOrNfdwGH\ngSiDP1iFlQqGtS5iGOtVzPs7jmG4HRhsQzQK0X5IOgZzVAfMM++mUIvt7bD0NUhfBc5D5SaIDkH3\nPEYN+EC4YpjxDfHRiwSea7sIT2MDCqE/IVba83XTxoxDm8AnbXjtoP/vd1cx5dt7jsC1YZ+nS/0Y\n9ucETo9w/9R9naO+jy9RUL9OeXmlwKRD8dwCRF6PAc9u+HM2w6/L7YYxrlJErHw/lvVrAP9Q3p5l\ne6jkLYjj/gyWL1CxtE2GeYoMoOwFqUBzAKndjs5FoIr8YIreXjEDfkrga5itGAN5yGwTAvIg6GFM\nbt5gFPV8QfI50Ismd9M/O8UNv/gyrppxefUAp1ZuI88ceg34RAM5p0RxxsGfvMDVoSm6aY3Bk8vo\nuxzLyRCsgvy2oK/6cd0COgm2IxJ4CYu3djky/xL6iuevOH4UbU/ZYiEeUzOtI9k8Or8KOcidw+gD\nQ0bmtJgifzWLXk1ABZFJLHRMMdpRSzZLNUNOKlqPTWdnl9B5v5gV9yCfhTwBV0OiKTSxsDyRxzEe\nDgdMIfIAqk1ff9b3KEX+FtVvYQ/3KEaNajkcRd6P6mEv93lUn/DnD2C5G0vjtQEjsgfLnwgWx/yc\n74dglKAtX0d5ejqMyF0Y30aOyFOozvtzjqF61MZLC+NICREac1goo+HkquN+vCHFmPq2khIGHzb7\ngGHee3y7inGcFBtyyn3c6vP672VejPXnwPXX93aQW1/e6Lb+/62z7Q33W8BVUvP4lngDFMo4qBkd\nVhrQ8viqCHpXpX915LSiXX+lKphn7vHqvtEG5Io32mC7LS/TdyiO/vxpopp9mU9HLdVYBFxylo8x\nc+RZxFk9blljgKXmiGHLAsxjWHjApgZLny9iXjNAq4u+NEegStVrY1CabtmPQJqb0Q4/3V235L8A\n5zswk/QdPdOZUHjDXm4wtjhw/zbQ+cK7lGwe487APO/wpiP2BjIYuJsJvBv+avXrV32MItrB4o3t\n2CSqhwi3jurzhM4WfQ19LwZtCVxDuYzqQkluZZNzwLzqmq8z9UZb/f89Jb3Y9nU/4DX1mee+PmGA\nnWeG2f8inVLbtVK7sqXRXl+2wlph63jo7c7Z7bHtXK/dumWvR263uvh+0Nlu9bnVObuVux5dbFfe\nEIx7u5KmBQdEKNZ5A4DNPhtVpIha768JJIokObo/eEcZLOdopkjmoQg/45UeqI+gkgwYtmrEJ4Se\n/9YEWRKRrcYMs2h197DNLVWMA6UKzIl5wxW1mbZ6rusBteS4YBTYPhuWpNhMG2+u4gpEVcQ5pBpB\ntgwhXlcxPhbBXIkoxDwLnOtBqha3PRYXckCgJTVvOKfPldEGzcXyWOYZ1J0/lvcNUsBnTbd2bqAX\nlShG9aqN1xntp2qGpfzKgUOYd13FYBKHxVyHVF49RIxpr2ir6/sajKv1NVxj+x5C9MpjtM9rvwtG\nwOSvPUJYWLP7xzb32LgseUBxfuTlHLY4uTEunD5Bk/V3c52plym3S0mOde2uPbbzGN8cua36tNu+\nf6/kdvq8k9zWx8IXe96up63vtS62Km8BV8mvUYDTUHh1Hht174K84n8fo48lHm7DeAeeaVkEBgkw\nDZLArXdBb9Bmtke7cCSB1wbMu61jvB8rwO0YjcYtMJAuMTi/zLWv7yePHXwigwVnuRlfsSa5Aahl\nyGSKPuCx9k814EVX0EysYu0OZDDagys+0mMMT7ehsH8JjijcNGJpv76KzQByLHoux65Yq2cziLwG\ngykcmINziaeaGKTAf+fBzUJ+FVwdxu6xlwzAyEvQXYZ2x+vQNrtYiShwzEH6OQ6bdZgYgcmjkEfw\n1GNYDGkbuB/zUjMKnPg+3+k/hv4mnCHMiJ/11zbwZIjvd5ewhd0w6cCkl2Jv3O3wVfF9GKJIHbbE\nRl6QOhasH7i3V32fOl5vAV/Htxvw8jmKnJBV38Zm3CQN38+deDGC//P9jH3/u1yGsdlqFVuz2Ylf\n5u1QtodK3gI+7t/B6C8FkQNoiI+r74WB49hW7DYsPgc+zEx+/A706JAZt6dyeMQvxzYUeSBDGwal\nyKNfR6++agb75pPwQ+8BcYZJ/zVoD3umjlDMqMcwYx74jiKC42U8/RfNu6aqBt3451nuEDREvn3p\nHDx7yeocH4H33GLbzXOQp0GDDX0Is3kptr/kK/QhELni+6dA+xKsnvNfKhifi4czRvaisd8J9I4U\nPhjbGK8uw7/4AnTDzCX2cAbYi/Lm0nXIMfxXvOce0acmVMxj1wSRSxg+LVgus9d8P4a94sohZOHv\nceyNFxRYDLKMcVvoXYBL2tgDtF5uzd1T+pvvIDeIrV7by8Fw/PASkVJf8ePJtqmPHY+V6xLZR5EU\n4RpbkVPtrr7vb7m3Y5+8BHZfRKVn5O3Rv62PbW+433SMO4oqpKliOGmB0Up9ChVvPdMWtnCpIKAn\nfJJDBLkg9GN5R4Fm1MeNdfoMoGYwTxxAK97zCbzxSkGVEbDwSdAySV35Ol4Cnx3Be72+3QEPxQTH\n6tVp8DSoTA5C1cv1MJw9tHujWl+rwDKI87kTU2+0QxO9qxTeWhUjGwJE/X1eRgAAIABJREFUzGiL\nABFyt0Nrvq2r15B8FQ1p0/qx1WAbX8ooWPE5vETJQTTwTTsKnDjcLBf8b0FB6zOWB8N6hOI2CokT\nQlv9T6yNhe5tIVcuwahvnxPR5Ib9i8tmGwXGrWvOt/OyHerbvqyVq2Iv2jCuzXNJrm9ru/JGyJX7\nuN0Y32i53fTnesobpzP1clsb7bebznYqbwHGXd6sUUw5tTMDmiH0IKqZ4QlJZy+tQKaQJOihHpBC\nJYeWGglUMIzjYXUyRl++bNh1DoxAf51MWcM55KHRYgnNUczgQyScYvCH3y9D4KPP1DYIHR7FvFcH\nsyuWxivD7FfFj1VzOJVbn7oJDCVonoBmFhdew8arKVSGMCNjkJAivu85pG37qzn6XKgvh31jaIn/\nuoCgBFUjjgq4tgYi8BKua7+Xf4vW3VB7fX3ODz70TyiMleLfdphh3+v1stmdsOrryClnsdmqGEOf\nK14068parHARi10PM4Lg2UfeGy7ybO60MFTGHneWC9lugnBjk3FsXs/1yF1vHW/sGHeW2+r79cqF\nstvxvhF1fK90tpPcTuUtwLg/iYHNIbdesKI+RreyAsl3gA4c/I9geAoGarB0HpbPwuUzQB3e9x8W\nZG5fxmblC4C0IGpBusciM34Gn3ZP4ZsJzAjkFSq3dajek9B6adCiRe7B1t8Ggc9jYcRXMIM6SpFW\ncB9mZxwwvwoLqzDXASKI65AaMx43YfBqF2gtQq8NWQr1LhychldftgXVk/8eNJtW58ULMH8OOi9b\nw417oXHU9LL4EmRLGOPWBLhRSFOopnAkhbMVSB3EVyFLzLj3jXcwYFL62/N/Q2aacGc7r4RVynkD\nTRFXMQ6PMN04hsVKN4BHMa98ya4PI1gc9na3k8OMfgj/GaLAmsuligW0H/LnPMLu+JdHKPhIxrAX\nyUFf/1PYVOzNwKH3EbbEF7wm11vCIvCb9jj+Q/m+KttDJW+B4f5dbHUfQhiIQQEPAu+3qasTGFEk\ncjbdXZ6BXg8hw8LIxpCKWPLa2y0jumbYgl/PTz+OA+82+FeXU/jjaaRrWWdO/Ok1hj+6CuqY++Nx\nzv3HNyKRoI6C/z+lv3lHHEb/Mew/Z5h9ytSM74BC3bKMa01gb5DL4dQ0JGnp+VOKSI8JxPkxTkjh\nca98BzrPIy5G80GQexHEe8QGM5nOzgJn7LMbgZGPWH25wFIGqe+TngK+48/pAVc9ZKDAfgo4Zj9w\niz+nixEiBQ/SFnHsWMP6LpH3gG/wSsuAZ4CZDSvm22N648Bd/nOGvQR66+QiP/4Qe725wd2uXavj\nBuCYvwYt4HH/eec6tpv+2ufI6zPMCq6VdLZbXTQwrnL89bnE+pfL9dX33cm9fl1cn9yb0ffvldyb\no7PtDfebjnHHceQx7pyAAaqCyEmMiyKyULuA/6pC1x5iJUJk0OQSYAAkV8ut6DCvWiyzpBw2Y6sA\n86mFEnpIa/jDq7iG4Sutr45AJnZsEDPGztcX8j4WEWD2OcM7sQZFUCvapQ5EHsJJM/OK1+hb/ANe\nNxw2921p8IQrkF7xbaXAAILXxRpsGkSuYXkVgXgUcZaQzF48riR3GcvTaPCU4bqhU7az0MLdJlAN\nL9VVipBDCMx02h9keJH4/HF+a3nYtFK+x7ZzBezYCAZjhJlAuolcWEDUTesLN/t2D52FN45jOSYj\nbKPO5lP33dW3Xq7iXw5h9tJ+HbqoAeEarMX+N6tj5/q2NkCvb4xvndz1jPGNlnu76Wyn8qZj3FnW\no4iXLciTVJ/CpsyppcvKWqAZqCKVAgMNcbig0Mqgk3mGdEWqHhKIFL3sxdIcRsQwcf8QzPz2IPmq\nkLeFwYcWkaoZcdo9pL1CSPIoYZ0teOD4Kpx51KFI4iEIzWHVXhLkRklrdYcXVUgOoBgpvsea8xxJ\n0+IKVk9QLAzOUp7Sl7E61UDur5BcgWweS4OTIpUlwkqs6hGKTSflBTShvICm6qcsZPg3UF/XxiQX\nSovCE+8h0iVg4yITm1/4dX0vPguwgEhCWBhY29bWpVzHVtj3+nZVL1JchyHK+PpauV11YZ1cj8LY\nrtfZ1n1ai7+2sZvNoC7D9jeT266Orfu42zG+0XJb9ed6ym7Hu53c96vOdipvEcYdUzz4IT43/NbA\n8NUaND4ISQXSLuYOh9jLFpYlxcc11xK717MY9ju4uQF3jIJE8JVzcOYatLqUsUc31aByS53uswO2\n4Df/BcxbVLjzB+D4FBytwf/X3rnGWlKVff631j7X7tPdp+9NA9IooCLvvA4Bh4yv8ZJ3lEQcPxAz\nyegkk/jJ6Ac1IgQFeUOURI2AMWP84CVm3k+vYqJRFHG4zCgqg9o2o8ilaaDBvtKnz6XPbe9a8+FZ\na9eq2qsu+3r2putJTs7eVf9al3/VXrXqX896nr+dgP8zB+OXQG1KmraKzMwn5sSDZHKb6NerS7Cy\nJN2aqsPqq2DOkfRV14grnPOqcOL5GKh16502joQ2/V+IRloD/qs9Jj0bXQB+TvNdQe2NEDk3lWms\n6w0yWJ9GNJ413CIa+fMHa41o2C4Gx0lcMCIpw/lRGyS8qbsRrBD7TZe1GnHcEhunoO3YH9uIY5is\nIPJbkSlEm3dPMelck92au+F1o5+7eDCVVQZDoHHf4T0O7EcpiZ8cRbK4Q2tFpPfBtv9udVctcUcM\nxDPzP9t948BFuKwpxj57qHGFueQCeMsl4uK2UIeHT0iGGhTmil2weUKkhRNPw4u/s3EQxoHrULUa\n1GqYxs9BHUMbTVR7M2z5z2itierrMPcHFAaUwWy+AiZ3oJUhWlGwAFpHRFEd+CPKpqV3zGodx/D1\nP8eeDseBBVvGHuA/2f4qRJ92Ln/PAC9ZjdaV4er5O0o1LLf/DngrWhuiaAl4HLd6VWbZ67b8GWDW\ntmndlgEikexB8jpiY0qfsbgaEuNEW9xxYDURVyIdY6IcF2lcujxlr5+avS7c9QOhuMzp8qS/JvA5\njcsrI9y+4rYX4/Lq7aS8XtSbp8kOA2cbhes3F0OhcddqikZDBlCJlaESel4UGRjfJT8m15zIasaA\nUido6rpM2U4lBSyzZlA7ZjAo0b+XbTJYF4B/0wRoLcLJuZNAZEmTGadpaJlRcwKoy7xpai8oLWFH\njMxAjbG+2+M236RR1s3Z2AFtzeKSHPixiP3PcT9WvDZtR17mupVBfnlz3nflXQgGcU1zOpr4cUt5\nK4mByr0EFI17EmOUxdVT3EqsDtm37rXdDZzYc+r2+f1NnJ6SXKRx6c+aWBcH9xQQ+jGFykve6Frr\nbVejzKo33PbiPua1vZPyyuCKOcvHbTRnG4EbBBdDoXHHjTAoJVlJAJSSRROgYP3vUD+D81dWE7Eu\nbsbeghqT+BrUajA2jXvkVcqlpVJweB61JNo301oy6UhNqGMrMjAbUNveiBqftfuWUcqG89SgZv4D\n1Kal7Og4ErcDqG1CTe7A6cRq+biVJxqosZMofYpYo7SBi5RCzczAuIuGOIXWEoVPYmy4PI4KcX3b\nZHGvolSs6ytlE0USodQOTy9zIV9ddVuJNd+nUeqcPW4LIoUoJPbIJcT36wWrNbsBWXvluVCpGqUu\nRqldds+a13ZQalvzOKVItM9vU1przMpFmI1r2HPl3hlMJXB5ZWRpm3l6aNb2suUVtakTXFnOypTX\nThlZx4S+d1PesHLWCZ9528vi8mxAGndzC+Kbuw3RaJeRH+A+YCvo/RI7A6C2FaZsqNNoCVaPw8Qe\nmJ6BTXWJMXLMrfhrAONS1K6z4md9bh3RfKfkr3YMNi/C2MWgN8HiM7C+JC9Ft++Crdthxy6RXU8u\nS0xrVmD1DIxvhtoWmF+0+vsK8DSoP4Bx+QP/yfYxgq3jMLsddrwezo7B8y4mxjzwb8isdxoJ4H0A\n8TdeQuJ+uIHQrZsfR+Jg/x0ZcGuIj7KL4/ESyTepbgUkiMbvIt25ONbTSKDyvxD71DseFfEqpGXb\nrquAt9o2/w9iHdfloJxGdO442p+sptxtMU8Sh0/shbmr2xDfvFborWZdWWUbbUOgcYuWCfBPaC2z\n7Ch6Cqepij/x+9BaWyllXzNTShQdAXUMpQxm6wy84yrZZyD6JWi7liPaC1yAuBUurcFTJ+3KeEUU\nPYbk2DNEE2+GmatFPqifgzMHJSOI1kT1q1C1GTAKEx0DDot/tpkA8+/RNYmZEkX/E6VeQjw49gBX\nWnkjAo7IXV5rovo7UfoiQGGip4AfSj+MBv6j5aJm8/5pYl9rp/9GwP9GMt5ERNEssCUhfUjGG3GZ\nS+fYE9wkcJHNuKGIoudRSqL0RdEZYN6eA0lw4DJzRNEriGauvfZFiXqlvIhYq/c1ZAVEaF2zbU/n\nckw+Jsb1lsXtADZZ3s8BJ1v0c1deqIwkZ+H8hek2ZeU59MvIx7Xbx/K49L5WXFhWqjjrL2eujPY5\n+8KwaNyyHjyK3LOL7ye8GaXcCyiQwUzFOKdxT4/L4CtjBqwY0ZkBtclgtLL+1MaWB9iocU2dfFxm\ntMYAUQPcBRNFwBSm4eoVqUHcmoWmqOEqPkUcG2STLU/hPGfi8rbFOruNBSsno+b10T36R4kLSE6w\nRKaLtTdxZfP12qRmHB8vepvUleTC18Lrni7nXhq79jbsD7Xhfcery+DkkvQF5hIVCK7hbSeFS5fX\nDk6Ws8q+RuKH7+NC2mMrZ6YQ5/gM4/C4SPLRXR/L49L7yuBauSiLg4qzdnHQDmdF1neNOza3NFFc\n0ZSabc7UlDqBrDdvIAP6H4njN+9Ba5uJ5PRxePkFaDRkkc6uUzRd147NoZfmwRjU2DqMORc2jUSO\nk2XbemUO3bCLO2ZnUPv3WBYawEGc5q0mLkBPztr2rSHpseq2/VciPukKrVftjNgNVv698Hcodcb2\nYxeS3VyD3gyTU1bUqqPUyWa9cf455we+pVmaUmfQWl7qxnqYG+Cdr7XIHIID8Uhx2/0IWADb0Npl\nL18jmb5rB86nuJlDk7AO57b5mmIeLs6BGLZkeWGcvAuweUZ1rXkthcxvU56O6Ooq0hrzcMk+UohL\n67D55ZXlLBvjl+cfk8YNkrNkvcXc5l0XPq5XnLl9g+YszwascWtkhlpDBokJxDfYabk1RC89A7wD\neDMygJ9EBnNX8BYwNj7GxF6JGbJ6At44AdfsgENz8KeTyLr1HcAbYGICahGsaogW4JJTsG8Wtk7A\n4w/D3ClAgd4H45dL2Fkm4Oxx2U4DeAGZOS8gA+oOaXNtM0yMQ+MkrL1APPgpmLjY5oM8DPVTMPF6\nGL9Q9PqF+6H+FPHLwQsQvX/M9tfF9CAujwuRkK2nES8YF9t6HLgU0ZWftvxebPmdRmJ1LNkyZnEJ\nFcTOEkfScu8FnHbdjp92r8zFIT9HuRgllVX2WrN8jbvvUgm4O4vGmAtxGbqjaJt9bFDID3W/HegN\nxlxn715jRNH/Q6nDiccYrRZALRHNvhtdmxQ3wP92EbzTyAKZN03An59AG4NSR2hsvRg9NoGhhuFF\nWH4ZXohQL7+EqR+RjOpaEUUXoxnHrP0ds7qEvARUVlJ42eq1u4iiXbFv8eRemLkUlEaZJczpF6nV\nRAKKZt6Lmtglbo4r47B4GrV+GOrPY5ZeFM3c+nPKcvOjSKyKpE5Xq4m+GEXvRKnXWT26hvi3R1Ym\n+C+2fZooWkTiab+EBImKPE16P1rXiN0yQV6ITgHH0HoFWCWKzth3DslHSPeo5+tyvv6Zj0u6XIVx\nu1Fqyl4XNeB0gou0Hpius5UzcnFpLdM3X5cM9THGdcJFLznL56IfnGVz0V/O0tLEsHPmJLxecObb\nADVuYxvn9vgDx5g3iCtkwHazwXP4cXRjfSwCNUXk4k5vt4O2UrC8JgPiugHqoKeaWrjzyQYwdeuD\nXHeNGvM0eN1ss4vfIfW6H7p7HhsHG+7U2M41XHNrmzDNoCdr8Yk1ssQ5asRXV8xF1HIBCH8Am4mD\n9q+m9LKJBGfxrD9K6Wj++wPfxKvE166jwGjm2pWn82XjWmttxY0R+2q3cpGlZWZzlo8LvSxy330d\nNtTHUJvKc9FLzsr1sQjXLmdpqzhrxblZcy84863vGnf8wzDI7MnFqFhA62VkNngSiSlRR+Jg/A7x\nI15HPCJkwYtSmzFmKzIjXYeFH6MaJyFah387jv7tqxJ/pL4IM2vIi7mtMH8C1ViHaAVqp9H6pC1j\niqbcwTji141t7wJaL9o2LSKSwbr9m0P8pOuotYPo1YMQrctKTe3StI3BwiF0/VUwqyi9AmrF9tcF\n73azyhm0nrZ93ISLJx23RSGn6hBanwbqaD2NMds9bh9GKRev5Eq0drGxp5EVki5O9kl7DsTkbu9y\nfyrL2SZkheoWW+8MWifb5G6wMIOLQVNW487Hnbaz/sjrd7i8UBkhDdLH+S+F/P/+LCsP12m9aWv3\nvYCvm7bLRQgX8m9ulzPBdc5ZqJ0VZ631h2wAGvddiO6afvkVsilE23T5Fl2c53VEn51BBrUziN/w\nSUTH3W+PX0RegC5b/AHEb/wfET/op5F0XHOIn/EuRA5xaa62kQjyv2077NwE86/A6aPEucteJY4D\nopD0Xf9s67TZcQB5mXkUeNZ+327bOm/rfLPt00v2uGXbvx22HWft9i3EGd4dBy7u80nil42bbB/2\nI3r185bHMdtePxel8+uOkBCuIDev19n6Zmz988g5W7Z1OXP+4ZtsvzdCC6+ssteqbbDGLTn5FOID\nvJDQcNwdJ/4v+qoxW9F6HWPWMWYB57csZcyg1E6U2kEUvZ5aTWQLY06g1DzGbEZCbS6h1Aso9RJR\npNB6iijah/gtn8WYkxa/F8mNqYiibbE+dsFFqAsuwugaavNuzGmZ2cqjzd/Q+px9xLkWGbTHUGoV\nY46jtXtM+gNaL1mcywOp0foC0dM1Vms+hNZnrDSxxWJruLCrWhtb3j771KFQasX22UkhoPUyxixj\nzN9xfuVKLeNcspzeVqtFNBpLSJhTZbmftFzUUWrOatxO2ppDqYXUuVpFqTWiaN7D+ec9Prdx+/I0\nylj2CeHceUn6E+drntnXWbJN+bhYe0zLKp3hsrlwfXytcBbLpP3jbKOusxCuqI/tcpZnfR+4tVY0\nGmGNyZnfiVYt3G1zGrixg518bjTc80vk4UBehrq0XTWvXj/nYIyXzzqut6Zp5raM8HAAdU//nbCD\nZLwoJm57g9iPuYZbmCI6uu8zve6V53AgC3X8F2fxs5ox9SZnYW6jjD6mdTmfsyxdLiqJo6VN2e2L\n9yc5C5fn9ie1x+x6i66zMm3K6qO/v31cdr1Ry3U22pyF9N9eczaI66wszq8r5qy1j+G2t3KWZ33X\nuBuNM8A6Wq/iXkKGzA22Sk0j0etaMUotIY/1a4jGfIo4rscuXEhTpa5CUqxvQ6lZRE93pbwekQNA\n/IBPI4PvLmC/1XKX4dhvMH//DazOoZafg7EXENlgHtjklfc4xjwKzKH184jLoIvl8Q8otRfn/mjM\nacTH+jjwG5Q6jsgdM15/j2GMSCvSlisRLX4d+BvideKeTGKtzP8fmySiEPnExb2etRxLih/RsWUG\nLW1Za36WdxDJUKNFum4I5yzkK1ukM7qLO0/T7ARXtu0hXN62UB87Kc9ZxVn7nOXxmNSa4895XHTD\nbTec5VnHM+5PfepTbN68mZmZGQ4ePMg999zD3r17A0gZ7PzZhDOTuLlIeiyJijeBMdsQzXUe8aSY\nwZgFW95Ze+wm5GXlrIfbgry0E41cUneNEUUziG48Z/e5GfJW4FokndYmJNzsumSlefkpeHkOwxkk\nyWWsEUeRc6FbAB4FHrV9dO2ZsvXvs58N4pp32t59JzDmJHLvnPe4MMjA7EKoGow5i/hrGzv4O9sN\nXIQs+X4BSTrhc+tSjcnLUuFnnDjBrfvs8BPAHiTx7jJR5Hyow6sf4zq2IHr3PMYsk2Wht/3F14WP\nm7B1Oc7Sfu7ly0vP7Hq1Lc+joejYkHXPWe9ww8hZXjt9C/VxENx2w0+edTxwz8zMcOeddwLw5S9/\nmS9+8Yt8/etfb8H5up3/CAH+tk0YswuaC0IuJs5TucninE4+7x37NuLUUS4t1QJOj41xEvtEpIk/\nodTTxKm73ovMTEUflvZeAEwiGrhCqQmMeb55NzRmL1qP25O3hrjfgfgfX0Mcq+MVtF6z/V8Ezth6\na4he7Vwiz3pc7MWYNwMG0eIftvtMirM9GPMW4qBTTwe4XUOptdS2RU+zWyHWuGcx5h8tF8Zy4ULN\nLuecv31oPebhlhMXX8xZsUYZz2biGBZxXWnO5nPa1Lttri2heMyhY7vB9Z6z3nKRrn8YOPP/DyNn\n3VxnedbxwO0GbYBGo8GWLVuCOGMetv9BvDwOeHsVBL1M3HZFPJgTwKb3p3HxvvjiiwL7Y31a/qnE\n/rS+63+OExT4+9zxJnhMa3muH8k+x3pkydtwwrK49cvNLzv5g20tr3WW0Mp3sv/xzad1X7h97uJu\n5cxxFW5TkZXHtZ7fbsotM1PslrOybWkXV9YGyVm4jG6us+L2FrWlE4ui54EjpQZtKBi4r7/+eo4f\nb00Ndeedd3LDDTcAMDc3xy9/+Uvuu+++YBnGvAvw7y7u0X0zEqhpHnnUP4VEvmtgzB8QLXoWmgt1\nVoilgE2I98Uy4rYGsB3JkPMSIkEs47Rs+BPx0u8178I6haQLuxbxqlhC5BmNaM3nkOQNryIyw7rt\nxwmcPCCyAva4cURSkRk77EcytczjfKklBvYkksh2zPZtFyIDLds+HkcCby0g0f3WU5wt47K3iz6+\nhDFTyOzf4RrEklK2xT+KOSQE68U4X3Vp7wRxcKzWmaFkwNlqcfWWWUW4LrdlHJGRXMjb9Qwc9mnr\nOEptxSVSzm5TUb3lcSErM/h2Um+v29RrLgbJmW959bZbl1/WMHGh1AGMOeCV+3BuGbkD989//vPc\ng8+ePcsnPvEJvvvd7zI7O5uLTZohOfMFmvkQI1z0PLE6sd82yCCxDxkYl4n9tvcR+02fs59ftuVM\nIj7Jixbrz9TWEP9kl5SgYf/WkUHsABInW1J+Cal1lDrj3YheB1yCuAMeReKM1IC9KLWIMSeQG4zz\nj7YstMwSjK37KLH/tKvDWH5mEWnEIIG5zqRwfsCrdu0kSV/tMlZHXmomregRW8xYWSZ5LYSOFVu1\nN+Xhtey2i7U7UyvHY3G9w2ztDszd1FE0+I6KdSyVnDp1ik9+8pN8+ctfZv/+/fzwhz/kxhtvbME5\n7Sa+y7iBMV4CLhq3ZJgxZgK4jFhuOIFS5zzcbsDYmemzxD/4Z2154i3hTOq9kPhGoL0TthW4EnnB\n5vDupnEZSl2IMbo5yw2ZUhdhzBsQV8IIGeBdm87ibhKSh1K1XDxisppR9O/5ZrtbOYtdBYWTM5aL\nNO5MUEfrZjaTV17ox1D0yCe4OhJXJRvjyi9qUxoXalPZtveTs6x+lnlML8NtO1yUwfm2UZzl4XrF\nWdnrwu0bBGd51vHA/b73vY9Go8GHP/xhALZu3RocuNMJWkMvDiwSmnkU0yK9afnvFn3EnZfjpa6Y\nCJdMNt4W+wDJbM/p1DIgxvXGs1b3otQ/ca4//mwxeYLdoiF3oltnlHF5KngSWzlzdfmaeFxeNreO\nC/cyRpHWRFs5I4jz8a6tRS+D0pwl+xjCZc+OQrhQeUUvecri8rjw26RUe5wVldcLznzHgE45C71U\nK77ORpezXlxnyd9S6yKjdjkL8jKYsK7u8X47Iju0PlqL1jmDPHqvIzrxNCIbrCHLs5cQPfQNyCDm\nwpGuIW55NUTemMG5Esq2WWQmuogsL/frd7PuGZKmkKXnY4gcEwqz6nDiAy5yzsvQDFNr058xb7Hi\n8hjP/p1FODfH2Fy6sUm7b8XWtRnR+BcRScgtPZ+2uCx3vEmEu2nv2Moqq2w47Y7cAXwAS97BmMXm\nTNofMJJ3mQnEBW8MWa7+rL1rjaH1LFE0gbygehX4g8VtR1z1JoAtaL2bKLrAlnsGcXerYcw88gJv\nGdGn/dnwPPB/kYHtYrtvFXkp+VeMOWq3bUYGXRDXwynkZegCSp1CltD7s/oIWd5e954MlhEXwQmi\naIJ4oc50CgfyIlRhzDRK7bYz+zm0XiSKFlM4N2uve3d6AuVJ2jSRZZK4Ipes1vLS5zj72PT5LosL\n1V+EK9v2XuNCXGw0Z+3iOtnWLmdlXf96zVm7188wcJZnA1ryXke8FuYS+2In9k2IH7FCNOZ1r/E7\niKJpi3PygEG8KiZxHgZwIVEkyQGi6BwyqzaIPr1qy5OXd63eCHX7t2jrBziK8xk3zYQM9vmJWe/Y\n1scyGbQjYCHgqB8RRS5pgbMkTk5eZG8gE14f6zm41cQJD9UrnK0Fcf5FnX4sDJfXis86Nl1GWZx/\nIRctlkg/9ma1vSwur51ludhoztrFZbWpl5wV9Sevj91w1u71UxbXT87ybABL3qUlTjOq1VTzs/uP\nzbeolAt5qNBa2/0NDycDt+BkVhuX10DSdLkkBPK/VpPP8fJWDZ4WDnIHlHojtHbHNyvF+Wr76aji\n8nyc26c8XLzfYdw2H6c8WHwXlv7Wam6/xk/RFXMW19XKbWu9oXPg/6/V4valrZWzZL1hLsLlKVXM\nWaiPWZz55YWvs9byirgYFc7y+thrzkLXWSecZfUxycVoc+ZfF2W5SPcxZANOXRayzfZvingQdHp0\nA9GeJxANe9n+udRWMxazYvFbgT1I/JEzxGFLlxBXPOdtsoKES21pMaIfTxLH33Ym2W9kn0Jm6Mu2\n3nbSa00Th6x9leTMO2Qa6ae2bWrkwyurrLLXgN3Bhmrc2TrfBFrvsNq1DNjxI0YNCYwEsIbWJ4ii\nZZTSyEIbly9xEZFfGvYueJooOu3V5aSZTcThUNdRajGjTQbRwpdQqoZSu4miaWTZ+ElksFeI/i1h\nZ91dOeyZMGn7OI4EyHoV0bnXkRed8YCf7QHgXlwW4eJa3YwgjfObLrqbAAAVA0lEQVT3+zOHIh1W\ncK3LgzstL5+zZB9deUW4LC464cwP/Zm285mzdrlI4nrHxWuZszwefRvAy0kFhHKo7SCKZNGLI8J9\nTh4/RxQt232TSDQ7NzOPAy5l6UliEtda9rmVmvk6mjFbMDZxgmjM/sKWc7namV9vFI3bMvxFJk5T\njy2to2W1rxtcax/LaYqCMyVxxeUV+XjnacNZuF5y5v/40nY+c1amvKw+9JKL1zJnQ6Vxax3SokSG\nkO2GONi/DI5O25IXg7He7e6kWhug1qIJ+Z+lrhrQQGtt78C1DJxqbpd9dcDXu00GjpbvMa6OS77g\n1xvS5fztro8hnN/2tN7mcLFG7peX1ADzOXM4X8svw1n7uDJcDAtnZbjw2/Da5oyKswLO0vp8J9dZ\nlm2Axu18id3M2fkeNxBN2mnH+xC9ehZxIXzcHi85GgW3VNCCPYgL315kKfdRYu28jI0jmvcqrVq0\ntu11wbX8FZO+OV/sc6RjW1dWWWWVhe0ONljjTqclEpc0rVcxpoEx657uM+8deQw4hlLbUGrdPr5q\nYAfGTEMzrsdKs2xfp5K6TiJyynHcy0ZfbwOFhHadtnWK+53M8JdQ6lWi6KxXnt8zcfeTFF7Zq6Ik\nxdgKSo2h1F4rDzUQvdwN5NMotQNjaii1glKnCGVY97XXPF1OqSkktdsYkiziBC5TfRIX4ixUHok+\nZuFkppCNc9/T5YXqK+pjHs6vtzxn8b68x+FR4Cyr7a3ldc+Zq2sjOcvv42hyVmQDWYDjzG+g+DK3\nbvfQ9v+cpwlNItlblP1LzoJbiXKDe7xS0tfbxEfaJeEFeRJwuDX8O14WuYIL7/OPM2YaieDnzJ99\nz1pJCMTvPFxgyD81bFs9bb2Bc2csKjPLkpxl1y1lZeNC+m9WfTEuv1159cRtym93GltWo8yzjeSs\nqF159cR1tV/eRnGW16ZR5izPBqZxO1NKfLTtt6a24zShGBffxcBpRXVcHBPp8HizvCSuVYuS8mKW\nXHmiXZsUziAySesxrWW0fpY2Zddlt3ptWsX5kEummjRnSW6KOVv16qqlOMviNtbb0ris/uZz2y5n\neWWk+9iKy+KiLK7c9dM7zvK42FjOVCYXSVzFmY/rjotWXJFtgMY9RRxvw8WUbqtURLuesJ9XkUFx\nEzK7fiXjuDFiTTrycArxz55C7mOrxLE8Iru/DEUuXdk4Els8FDPE+WS7+Cq+jROHqu2Fr/aYbc8K\naQ+WyiqrbNjtjtynhQFr3DuRmB8KebEYSxi+XpSlbck+gwTvV0j6Lic/nEMSHmSVV8fF5E7uM4gW\nrpD4J86bZALYjfiUN1DquN2Xbt84EktkzO47hcu7mI2LbHnrHm4d39OmHBd5OFnCX4TL2tcJLq3Z\nDareYi56i6s4ax9XcdYdLm19l0r8peHxoA1KLSAz2lZLExU2g2SHcbglXOLbvPLEpTCU/NbYwdPY\n7ZvtIKuQJfnhhLmSsHjc4ur4yXKTODcbV15dIVx22/P0sE5xWXUX6XlZn8vgypZX1KYyuIqz7H1Z\nuIqz7H1ZuF5zVmR9H7jr9Th2iMwoIyTK3wSQvHumOxUnhnWySxonWq5cGLJkXjxPQFZJqlR5xZ/j\n76vNtjqayuFUC1Y+r2FMhIv9HfInz+ciPOMYBK7ocy9wWfuGjYtBcdZNGcPGRcVZ+7gi2yA/bk3s\nETJGWIOdJM4tGSHugSHcZmR5/BiiDS/ZbTV7TDtxRFp6gEQFjPMhZuNczsc8fdrh1ql058oqqyzb\n7mAI4nH7n91AOoMkVgAZyI7jZArBuVgeDeTF334P50ssS8iLRNU8HuaQONzdvOTbDvwDcgOoo9Tv\nbZtCZnAvI/N1qrK42HqB63VdZW2Qfew1ruKsO1y/y+ikvGHEdcpF36WSWi2uIqn1uIh3GrcwphVn\nSPpt1wn7JBtcSNd48A4P2uUfS3YjTwc1ROYot+ox7ySE+1gel9f2sjpa1vH9sE60wrT1mouKs8Hg\nymzvlY0yZ53aADTurBeQS8QJB8ZzXl4sEs+wx3HBolpx+d/bw9WQyILG1j1B2YeTvBPT7QXW2z6W\nx/XbOuFso7ioOOsfrt82SpwVWd+lkmxbQNzVJgjncnTmpBDnu70fiQtSRiMeRwbfdvTkLUjeyn3I\noH0QcSMsJ7ts1EU5ylZx1r5VnLVvryXO+j7jhrzHCINSqyVxJ5BEv0dRqpGBc59rwEUotQ8Z6Ccz\ncGnbCWxHqXPAIeARlDpDGdkl727e6VvyYcalbZC4YeOi4qx/uLSdb5xlWd8H7rExFXw8cI1LvrjM\nw7kXl6blbWtreeMopa2sonCeJf5h4buv6OlS/gp+fsqQFZeX3JfVx7K49jnrDS70OW39wg0bFxVn\n/cO108de44aViywbWM5JyBbs09Y9bs3+GfvnB3fKLiNeFGSQjPMqA5dXRjYu65g8Gxxn2bi8ff2e\nfWQds1FcVJz1D5e373zjrMj6rnHn3/k0ImOs4ocd7f5OGmHMMUQyMbgXoNLdFbstVN5ZxGdbXACz\n6io7Wxi2WcUgcBVn7eMqztrHnW+cpW0gGnc4atssokPvRlzvWu+IWdkzlEp+z86y4TK/7wX2ofVu\nW28a50cgM2hd9/aVq7dTXCh7RhgX7mNZztJZRjppeyfnoFPO8rlQwX350QGz29ctZ3m4QXI2yOss\nr163L+8c9IKz/v8228dltT3v+k7jykQH7HjGfe+99/Lkk09yxRVX8Otf/5pbbrmF6667rgVXq6mE\nXGKMu7PIEnX5XEeWt7filPKPib/75ife9HFxDGBZrSnfW/XudKB1P3ZwXjznXuBC8YeTbU/2K41L\nb8/iLB0P2ecsL8B9Vr96gcvjLHl+ktt9zvy253GW1cdecBbChfrRb84GeZ3524vOQb846/9vs3Vf\nUR/Lclb0Gy6yjgfutbU1vvGNbzA5Ocnll1/O7bffzgMPPJB7TLKRKyg1aS8oF8zJBHDJ71mfQ9/j\n7WcxZiug0XoSY84Rv+zMLts/Sf3E+d8drv0+9pqzeHs66/n5zJmbGb3WOCviJrTdH7B6wVka1wsu\nui3P/57HWZqLbjkrso4H7ptuuqn5+ZlnnuEtb3lLEJeebcvsdxOwGYmkdwrRpEnhWj9D+Ttzct88\nol3rlpRgefVKSrOdwAKif2fhypZX3N6yuLKfoVPOwscX1dstF8POWVkuRo2ztJXlKavPnXJRFtfJ\nOR0lzoosd+C+/vrrOX68NdHBnXfeyQ033MDx48f50pe+xJ/+9Cfuu+++jFIe9j4fQOtLgXmiaA5Q\niHuf7JVMEvLdaXKh/HP+vrycfT5O7r7xDSI9O3JlxHfpC4ErEAlnBfgtLntNEhcqL11vMS7UJndS\ni7joL2dZbQ9x1hsuBstZOS6GnbP0voqz/nLmBvHi35whioo5M+Z5jDmS+3TiW0+iAz700EPccsst\n/O53v0sWrhS12r8kZt2ZDSn5mNDJY29ndjnwOkAhqzwfJyt+eK9tUFz0nrONs426firO2scNo/X6\nfHd/nd1B3tDcsVfJV7/61ebnAwcOcPjw4SAuq26l4reneW9RBaeanwMI+38arVtXSPrluLpcfXk4\npV5G61eJB+vJDFxx+9vFpbf538twJvvzOCuHa5+zpPdCPi67TWVxIS7yOOuGi2R5/eGsGJffrnZx\n6W3+915yJrjs8vp7nZXDFZ3zdJsGwVmedaxxv/jii3zmM59h165dHDx4kG9/+9tBXNpjw5mvF+Vl\ngBacaX6Oc0fWkTgmNWAKY2Ys7njwZhGqKw8nLzD/CBk5J9vVvdrBZbWvc846w7XPWVxeVn0xLr9d\nZXCuXUXeKSFuQ3VuNGfFuPx2tYvLal9/OMsur7/XWW+vx6z29ZqzIhtIIgVft/F1n9Bjg8PVaqIH\nGePjJoG9SBZ1aDReQmtZAi/7k4Osryv5Gp1fn2uTUi4jvWq52fg4iPW79OBZBtfKRazL5XFhTKec\nxVwopZp9THMxTJzl9bEIp5TUUZYzv4+jxpn0sSxn2VwMkrO4j51xlocrw1l711n3nCnV2sdynN2R\ne9Pp+8DdW417Gkm4654xXui2iQO1bvWxfuOG0SrO2reKs/Zt+LjIH7j7vnLSf4vq/4ekRunamIdT\nahVxy2ug1DowkYGLt+WX19re0AqpIr0tVEeZNnWDK89ZeVy63nY5K9L5BslZd9dZ/znz8RvFWZk+\nVpz1l7NQm8vYBuScrKyyyiqrLN82eMbt7iDx3Ui1bAvdeXxc6L/TqkIxGDrD0SYuu6/+nT70Vtvv\nfx5uFDlLt70sF/3kLDSbGSbOQue2t1wMK2etbWr3Ouvf9dMbznwu2uUsz/o+49b6XzI9S9KPHlkt\nydvXWbs2RrPrRb1unzvpFWfFuOo6C+/rBRe9bntZe+1zNiQad5GPY54mFLK8GUF4lpBdV9axId7y\n2lekmeX1sSzOx/Sbs7w2FeFC9YaeUspy1g23vpXBFfWxLK5dzoquW2fdcOZbL66fUP3DxK2zXnNW\n1me7F1yErO8DtzPnnuP/sEM/cretG1xoW8jvuehYZ6ETHMINso8h6zVneWUU4UKchc5BWc56zW1o\nX7+4KIsLHTNMnHXDT2jbILntNWe94LaT68JZ3wfu9Cqh8ndIlYvrZsbdLs639LFF9fv9zzs2tJqq\n3dnw+cZZL54gKs56/9tM7yuqoxvOwrj+/+bS+9o5tt06QjawGXe7elSvpfeyxZWdCWU9cqXLCMVB\nDt+ZWze+ljnLK6MsZ520pRU/3JyVxXTTj2HnrN2nlND1E/ru48oOmMNiA/fjLno8CBHY/onL3ter\n8vxHpTKP4p30cRg5K7J2H1d9S/e3Gy6GlbOyj9PdtCl/sGrd1i/OupE7imxUOCuqN2tfkQ1sxu2s\nkztbL+6GRY857R6b5w5Yto6iH0WZff20burNe6mWVUeZmXnek04WbpBWVG/e/rKctVvuRnFW9vdQ\ncdZ+eQPTuAcx68krz7duZm955eYFfioqz8eUmXmG2hLChQbGQXBW9DLYWbucZbXttcpZWR7z6h0E\nZ2VxRbPrXnIW6mOWDSNnedb3gdtPEQZJx3ZneS8YsnB5Duv+DzB22ymHK+vkX1Re3iAQ4qIsLl1X\nEpd/u+41Z2XOVRYX+bgYeL5zVnahV4iz0GKSbjgr8xvx9w+Ss9CCGV8CKfvb7D1nxVwk682/Hpv4\nUqguLH0niaLWbaG7q79oJ4Rz+/NwxvihP9vFHQniQu0Llev3Nwvnc5HnXtQdZ0ea23rNWZlzVZaL\nfG6PDJizGNc7zo4MmLNk2NtecBZFRwrb7u8f5HWW7GPRb/NI85i09Z6zYi6S9ba2PWQDW/Iemm11\nEiSoDK5seXkzQDhSaqaYVUdeXZ0sqiiDC/fxSElc2fJa21SWi845OzJQzvpznR0Jtinr2PS+Itwg\nrjPXh15z5h/by+ss+2nvSGZdw3Sd5dnANW7f/DuZa3D+3agcrkgfy/NuKDq2XVyoj0WLKtJ9LIvL\n6uMoc5beloXrJWehgP695qyojvS+ItwgOAu1qRec+cf28jrzZ+vD+Nssew2ErO8Dd6NhWnSqLO3I\n171qNR+nAjiVWZ5/Jw/hnGXh0ua3vV1cvj6mgndp18d2OSvGleOsVusfZ9nlhTkL47L72N111lpn\n2evH5yy77YO5zsK41j62y5nbNuqcZfXR31ar9YYz18duOAvZAMK6VlZZZZVV1q7lDc0d55zstuLK\nKqussso6s4EvwKmsssoqq6w7qwbuyiqrrLIRs2rgrqyyyiobMeurxj0q9uCDD/KjH/2IPXv2oJTi\n9ttvT+z/3ve+x7e+9S2mpqYA+OhHP8pHPvKRjWhq0I4dO8bnP/95/vznP/P73/++Zf/Kygqf+cxn\nuOiii3jmmWe45ZZbuPzyyzegpdlW1IdhPwcAzz33HLfddhtXX301R48eZefOndx2220JzCicizL9\nGPbzYYzhhhtu4LrrrmNtbY3nnnuO73znO832wmici0wz57ktLS2Zyy67zKytrRljjLnxxhvNr371\nqwTme9/7njly5MhGNK+U/eAHPzA/+clPzDXXXBPcf9ddd5mvfOUrxhhjDh06ZN7xjncMsnmlrKgP\nw34OjDHm8ccfNz/+8Y+b36+88krzxBNPJDCjcC7K9GPYz0cUReaLX/xi8/sHP/hB86//+q8JzCic\niyw772fcjz32GJdccgnj4+MAvP3tb+enP/0p73nPexK4b3zjG+zbt49z587xiU98gu3bt29Ec4N2\n44038vDDD2fu/9nPfsZdd90FwFVXXcXBgwdZXFxkZmZmQC0stqI+wHCfA4Brrrkm8T2KohaOR+Fc\nlOkHDPf5UEpx6623AlCv1zl69ChvetObEphROBdZdt4P3CdOnGDLli3N71u3buXEiRMJzDvf+U5u\nuOEGdu7cyf3338+HPvQhHnzwwUE3tWPL6uMoXKDORu0c/OhHP+L666/niiuuSGwftXOR1Y9ROR8P\nPPAAd999Nx/4wAe4+uqrE/tG7Vz4dt6/nNy7dy8LCwvN72fPnmXv3r0JzIEDB9i5cycA7373u3nk\nkUdGykd9z549zM/PN7/Pz8+zZ8+eDWxR+zZK5+Chhx7ikUce4e67727ZN0rnIq8fo3I+3vve93L/\n/fdz+PBhvvnNbyb2jdK5SNt5P3Bfd911vPDCC6ytrQHwm9/8hve///2cOXOmOaDfeuutNBoNAJ55\n5hkuvfTSoV8V6rf//e9/P4899hgAhw4d4q1vfetIzCpG8Rz89Kc/5YEHHuCee+7hlVde4be//e1I\nnouifgz7+fjrX//Kz372s+b3AwcO8Pzzz4/kuQhZX5e8j4o9+OCD/OAHP2D37t1MTExw2223cfPN\nN7Nz504++9nP8vWvf50nn3ySSy+9lEOHDvHJT36St73tbRvd7KY9+uijfP/73+cXv/gFH/vYx/j0\npz/NF77wBXbs2MHNN9/cfHt+wQUX8Oyzz/K5z32Oyy67bKObnbCsPozKOQB44okneNe73sW1116L\nMYalpSU+/vGP85e//GWkzkWZfgz7+Th8+DA33XQTV199Nevr6zz11FPce++9fO1rXxupc5Fl1cBd\nWWWVVTZidt5LJZVVVlllo2bVwF1ZZZVVNmJWDdyVVVZZZSNm1cBdWWWVVTZiVg3clVVWWWUjZtXA\nXVlllVU2Yvb/AbtA5D2uJe3eAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb8ee76c>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%cython -l gsl -l gslcblas\n",
      "\n",
      "cimport cython\n",
      "from cython_gsl cimport *\n",
      "\n",
      "import numpy as np\n",
      "from numpy cimport *\n",
      "\n",
      "cdef gsl_rng *r = gsl_rng_alloc(gsl_rng_mt19937)\n",
      "\n",
      "def multinomial(ndarray[double, ndim=1] p, unsigned int N):\n",
      "    cdef:\n",
      "       size_t K = p.shape[0]\n",
      "       ndarray[uint32_t, ndim=1] n = np.empty_like(p, dtype='uint32')\n",
      "    \n",
      "    # void gsl_ran_multinomial (const gsl_rng * r, size_t K, unsigned int N, const double p[], unsigned int n[])\n",
      "    gsl_ran_multinomial(r, K, N, <double*> p.data, <unsigned int *> n.data)\n",
      "    \n",
      "    return n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sample = multinomial(np.array([.3, .2, .1, .1, .3], dtype='double'), 500)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.bar(range(5), sample, align='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<Container object of 5 artists>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xc75a3ec>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Speed comparison"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "See http://pyinsci.blogspot.com/2010/12/efficcient-mcmc-in-python.html\n",
      "\n",
      "Pure Python version:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random, math, numpy\n",
      "\n",
      "def gibbs_python(N=20000, thin=500):\n",
      "    x = 0\n",
      "    y = 0\n",
      "    samples = np.empty((N, 2))\n",
      "    \n",
      "    for i in range(N):\n",
      "        for j in range(thin):\n",
      "            x = random.gammavariate(3, 1.0 / (y * y + 4))\n",
      "            y = random.gauss(1.0/(x+1),1.0 / math.sqrt(x + 1))\n",
      "        samples[i, 0] = x\n",
      "        samples[j, 1] = y\n",
      "    return samples"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit gibbs_python()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 56.9 s per loop\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit gibbs()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 2.48 s per loop\n"
       ]
      }
     ],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}